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Scalar curvature along the Ricci flow Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-15 Yi Li
In this note, we prove a well-known conjecture on the Ricci flow under a curvature condition, which is a pinching between the Ricci and Weyl tensors divided by suitably translated scalar curvature, motivated by Cao’s result (Commun Anal Geom 19(5):975–990, 2011).
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On bounded paradoxical sets and Lie groups Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-14 Grzegorz Tomkowicz
We will prove that any non-empty open set in every complete connected metric space (X, d), where balls have compact closures, contains a paradoxical (uncountable) set relative to a non-supramenable connected Lie group that acts continuously and transitively on X.
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Trisections obtained by trivially regluing surface-knots Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-13 Tsukasa Isoshima
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Betti numbers of nearly $$G_2$$ and nearly Kähler 6-manifolds with Weyl curvature bounds Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-12 Anton Iliashenko
In this paper we use the Weitzenböck formulas to get information about the Betti numbers of compact nearly \(G_2\) and compact nearly Kähler 6-manifolds. First, we establish estimates on two curvature-type self adjoint operators on particular spaces assuming bounds on the sectional curvature. Then using the Weitzenböck formulas on harmonic forms, we get results of the form: if certain lower bounds
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Branching laws of Klein four-symmetric pairs for $$\textrm{Sp}(n,\mathbb {R})$$ Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-11 Jiaying Ding, Haian He, Huangyuan Pan, Lifu Wang
For the real symplectic groups \(G=\textrm{Sp}(n,\mathbb {R})\), we classify all the Klein four-symmetric pairs \((G,G^\Gamma )\), and determine whether there exist infinite-dimensional irreducible \((\mathfrak {g},K)\)-modules discretely decomposable upon restriction to \(G^\Gamma \). As a consequence, we obtain a similar result to Chen and He (Int J Math 34(1):2250094, 2023, Corollary 21).
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Topological aspects of the space of metric measure spaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-11 Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.
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The Nielsen realization problem for high degree del Pezzo surfaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-08 Seraphina Eun Bi Lee
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On the Teichmüller stack of compact quotients of $${\text {SL}}_2({\mathbb {C}})$$ Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-04 Théo Jamin
This article aims to pursue and generalize, by using the global point of view offered by the stacks, the local study made by Ghys (J für die reine und angewandte Mathematik 468:113–138, 1995) concerning the deformations of complex structures of compact quotients of \({\text {SL}}_2({\mathbb {C}})\). In his article, Ghys showed that the analytic germ of the representation variety \({\mathcal {R}}(\varGamma
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Halfspaces and hypersurfaces in the bidisk Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-03 Virginie Charette, Youngju Kim
We construct a halfspace in the bidisk, whose boundary acts like a bisector. As an application, we build a fundamental domain consisting of such halfspaces for the action of groups that project to Schottky groups in both factors.
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Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-03 Martin Bridgeman, Kenneth Bromberg
We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of the geodesic. One application is to cone-manifold deformations of acylindrical hyperbolic 3-manifolds.
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Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-03 Jacob Bernstein, Arunima Bhattacharya
We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show a relationship between an appropriate formulation of Colding-Minicozzi entropy and a quantity we call the CR-volume that is computed from the asymptotic geometry of such submanifolds.
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Boundary metric of Epstein-Penner convex hull and discrete conformality Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-03 Xin Nie
The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a convex set in the Minkowski space. It works in the de Sitter and anti-de Sitter spaces as well. In these three spaces, the quotient of the spacelike boundary part of the convex set has an induced Euclidean, spherical and hyperbolic metric, respectively, with conical singularities. We show that this
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Continuous deformation of the Bowen-Series map associated to a cocompact triangle group Geom. Dedicata. (IF 0.5) Pub Date : 2024-04-02
Abstract In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on \({\mathbb {S}}^1\) tightly associated with this group. In general, their fundamental domain enjoys what has since been called both the ‘extension property’ and the ‘even corners property’. We determine the
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Prym representations of the handlebody group Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-29
Abstract Let S be an oriented, closed surface of genus g. The mapping class group of S is the group of orientation preserving homeomorphisms of S modulo isotopy. In 1997, Looijenga introduced the Prym representations, which are virtual representations of the mapping class group that depend on a finite, abelian group. Let V be a genus g handlebody with boundary S. The handlebody group is the subgroup
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Mirror stabilizers for lattice complex hyperbolic triangle groups Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-26 Martin Deraux
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K3 surfaces with two involutions and low Picard number Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-13 Dino Festi, Wim Nijgh, Daniel Platt
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A geometric characterization of cyclic p-gonal surfaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-13 Daniel M. Gallo
A closed Riemann surface S of genus \(g\ge 2\) is called cyclic p-gonal if it has an automorphism \(\rho \) of order p, where p is a prime, such that \(S/\langle \rho \rangle \) has genus 0. For \(p=2\), the surface is called hyperelliptic and \(\rho \) is an involution with \(2g+2\) fixed points. Classicaly, cyclic p-gonal surfaces can be characterized using Fuchsian groups. In this paper we establish
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Left-invariant distributions diffeomorphic to flat distributions Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-13 Sebastiano Nicolussi Golo, Alessandro Ottazzi
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Quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06 Kingshook Biswas
Hyperbolic fillings of metric spaces are a well-known tool for proving results on extending quasi-Moebius maps between boundaries of Gromov hyperbolic spaces to quasi-isometries between the spaces. For a hyperbolic filling Y of the boundary of a Gromov hyperbolic space X, one has a quasi-Moebius identification between the boundaries \(\partial Y\) and \(\partial X\). For CAT(-1) spaces, and more generally
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Rupert property of some particular n-simplices and n-octahedrons Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06 Pongbunthit Tonpho, Wacharin Wichiramala
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The residual set dimension of a generalized apollonian packing Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06 Daniel Lautzenheiser
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Curvature bounds on length-minimizing discs Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06
We show that a length-minimizing disk inherits the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.
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Cusped Borel Anosov representations with positivity Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06 Gye-Seon Lee, Tengren Zhang
We show that if a cusped Borel Anosov representation from a lattice \(\Gamma \subset \textsf{PGL}_2({{\,\mathrm{\mathbb {R}}\,}})\) to \(\textsf{PGL}_d({{\,\mathrm{\mathbb {R}}\,}})\) contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov
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Homogeneous semisymmetric neutral 4-manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-03-06
Abstract We determine homogeneous semi-symmetric neutral manifolds of dimension 4. We also describe all the possible semi-symmetric curvature tensors on four-dimensional neutral vector spaces.
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Infinitesimal symmetries of bundle gerbes and Courant algebroids Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-26
Abstract Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) be closed differential form with integral periods. We show the Lie 2-algebra \(\mathbb {L}(C_\chi )\) of sections of the \(\chi \) -twisted Courant algebroid \(C_\chi \) on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \(S^1\) -bundle gerbe with connection (over M) whose 3-curvature
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The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-26 Marcos Salvai
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A family of Andrews–Curtis trivializations via 4-manifold trisections Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-19 Ethan Romary, Alexander Zupan
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Complete Calabi–Yau metrics from smoothing Calabi–Yau complete intersections Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-19 Benjy J. Firester
We construct complete Calabi–Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection \(V_0\) that is a Calabi–Yau cone, extending the work of Székelyhidi (Duke Math J 168(14):2651–2700, 2019). The constructed Calabi–Yau manifold has tangent cone at infinity given by \({\mathbb {C}}\times V_0\). This construction produces Calabi–Yau metrics with fibers having varying
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A cyclotomic family of thin hypergeometric monodromy groups in $${\text {Sp}}_4({\mathbb {R}})$$ Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-19 Simion Filip, Charles Fougeron
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On branched coverings of singular (G, X)-manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-17 Léo Brunswic
Branched coverings boast a rich history, ranging from the ramification of Riemann surfaces to the realization of 3-manifolds as coverings branched over knots and spanning both geometric topology and algebraic geometry. This work delves into branched coverings “à la Fox” of (G, X)-manifolds, encompassing three main avenues: Firstly, we introduce a comprehensive class of singular (G, X)-manifolds, elucidating
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Unique continuation problem on RCD Spaces. I Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-15 Qin Deng, Xinrui Zhao
In this note we establish the weak unique continuation theorem for caloric functions on compact RCD(K, 2) spaces and show that there exists an RCD(K, 4) space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point . We also establish frequency estimates for eigenfunctions and caloric functions
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The Borsuk-Ulam Theorem for n-valued maps between surfaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-14 Vinicius Casteluber Laass, Carolina de Miranda e Pereiro
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Coregularity of Fano varieties Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-10
Abstract The absolute regularity of a Fano variety, denoted by \(\hat{\textrm{reg}}(X)\) , is the largest dimension of the dual complex of a log Calabi–Yau structure on X. The absolute coregularity is defined to be $$\begin{aligned} \hat{\textrm{coreg}}(X):= \dim X - \hat{\textrm{reg}}(X)-1. \end{aligned}$$ The coregularity is the complementary dimension of the regularity. We expect that the coregularity
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Counting conjugacy classes of fully irreducibles: double exponential growth Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-07 Ilya Kapovich, Catherine Pfaff
Inspired by results of Eskin and Mirzakhani (J Mod Dyn 5(1):71–105, 2011) counting closed geodesics of length \(\le L\) in the moduli space of a fixed closed surface, we consider a similar question in the \(Out (F_r)\) setting. The Eskin-Mirzakhani result can be equivalently stated in terms of counting the number of conjugacy classes (within the mapping class group) of pseudo-Anosovs whose dilatations
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Topological and dynamical properties of Torelli groups of partitioned surfaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-02-07 Hyungryul Baik, Hyunshik Shin, Philippe Tranchida
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Entropy of real rational surface automorphisms: actions on the fundamental groups Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-30 Kyounghee Kim, Eric P. Klassen
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Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-30 Nicola Cavallucci, Andrea Sambusetti
We prove a quantitative version of the classical Tits’ alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geometric consequences, as uniform estimates on systole, diastole, algebraic entropy and critical exponent of the groups, will be presented. Finally we will study the behaviour of these group actions under limits, providing new
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Real structures on root stacks and parabolic connections Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-30 Sujoy Chakraborty, Arjun Paul
Let D be a reduced effective strict normal crossing divisor on a smooth complex variety X, and let \(\mathfrak {X}_D\) be the associated root stack over \(\mathbb C\). Suppose that X admits an anti-holomorphic involution (real structure) that keeps D invariant. We show that the root stack \(\mathfrak {X}_D\) naturally admits a real structure compatible with X. We also establish an equivalence of categories
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Circumcenter extension maps for non-positively curved spaces Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-30 Merlin Incerti-Medici
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Homotopy equivalent boundaries of cube complexes Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-27 Talia Fernós, David Futer, Mark Hagen
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Intersection theory and volumes of moduli spaces of flat metrics on the sphere Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-27 Duc-Manh Nguyen, Vincent Koziarz
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On Tholozan’s volume formula for closed anti-de-Sitter 3-manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-23 François Labourie
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From $$L^p$$ bounds to Gromov–Hausdorff convergence of Riemannian manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2024-01-03 Brian Allen
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Knot groups, quandle extensions and orderability Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-29 Idrissa Ba, Mohamed Elhamdadi
This paper gives a new way of characterizing L-space 3-manifolds by using orderability of quandles. Hence, this answers a question of Clay et al. (Question 1.1 of Can Math Bull 59(3):472–482, 2016). We also investigate both the orderability and circular orderability of dynamical extensions of orderable quandles. We give conditions under which the conjugation quandle on a group, as an extension of the
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Median quasimorphisms on $${{\,\mathrm{{CAT}}\,}}(0)$$ cube complexes and their cup products Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-23 Benjamin Brück, Francesco Fournier-Facio, Clara Löh
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Relations with a fixed interval exchange transformation Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-15 Magali Jay
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Moduli spaces of polygons and deformations of polyhedra with boundary Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-13 Sasha Anan’in, Dmitrii Korshunov
We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we conclude that a generic equilateral polygon
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Vanishing theorem on parabolic Kähler manifolds Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-13 Teng Huang
In this article, we consider the semipositive (resp. nef) line bundle on compact Kähler parabolic (resp. hyperbolic) manifolds. We prove some vanishing theorems for the \(L^{2}\)-harmonic (n, q)-form of the holomorphic line bundles over complete Kähler manifolds.
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Correction: An improved bound on the optimal paper Moebius band Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-13 Richard Evan Schwartz
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Low dilatation pseudo-Anosovs on punctured surfaces and volume. Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-09 Shixuan Li
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Harmonic maps between 2-dimensional simplicial complexes: conformal and singular metrics Geom. Dedicata. (IF 0.5) Pub Date : 2023-12-09 Brian Freidin, Victòria Gras Andreu
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Inversion maps and torus actions on rational homogeneous varieties Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-29 Alberto Franceschini, Luis E. Solá Conde
Complex projective algebraic varieties with \({{\mathbb {C}}}^*\)-actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational homogeneous varieties endowed with a \({{\mathbb {C}}}^*\)-action with no proper isotropy subgroups.
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On a convexity property of the space of almost fuchsian immersions Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-28 Samuel Bronstein, Graham Andrew Smith
We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we
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Construction and characterisation of the varieties of the third row of the Freudenthal–Tits magic square Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-28 Anneleen De Schepper, Jeroen Schillewaert, Hendrik Van Maldeghem, Magali Victoor
We characterise the varieties appearing in the third row of the Freudenthal–Tits magic square over an arbitrary field, in both the split and non-split version, as originally presented by Jacques Tits in his Habilitation thesis. In particular, we characterise the variety related to the 56-dimensional module of a Chevalley group of exceptional type \(\mathsf {E_7}\) over an arbitrary field. We use an
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Clifford structures, bilegendrian surfaces, and extrinsic curvature Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-27 Graham Smith
We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in Riemannian and semi-Riemannian 3-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an application, we provide full classifications of both complete and compact immersed bilegendrian surfaces in the unit tangent bundle \({\text {U}}\mathbb {S}^3\) of
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A Fano compactification of the $$\textrm{SL}_2(\mathbb {C})$$ free group character variety Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-23 Joseph Cummings, Christopher Manon
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Rigidity of geometric structures Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-20 Ursula Hamenstädt, Frieder Jäckel
Geometric structures on a manifold M arise from a covering of M by charts with values in a homogeneous space G/H, with chart transitions restrictions of elements of G. If M is aspherical, then such geometric structures are given by a homomorphism of the fundamental group of M into G. Rigidity of such structures means that the conjugacy class of the homomorphism can be reconstructed from topological
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Divergence of separated nets with respect to displacement equivalence Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-17 Michael Dymond, Vojtěch Kaluža
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Tent property of the growth indicator functions and applications Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-14 Dongryul M. Kim, Yair N. Minsky, Hee Oh
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On the cohomology of character stacks for non-orientable surfaces Geom. Dedicata. (IF 0.5) Pub Date : 2023-11-10 Tommaso Scognamiglio
We give a counterexample to a formula suggested by the work of Letellier and Rodriguez-Villegas (Ann l’Inst Fourier 36, 2022) for the mixed Poincaré series of character stacks for non-orientable surfaces. The counterexample is obtained by an explicit description of these character stacks for (real) elliptic curves.