Abstract
We compute the Nielsen–Borsuk–Ulam number for any selfmap of \(n-\)torus, \(\mathbb {T}^n\), as well as any free involution \(\tau \) in \(\mathbb {T}^n\), with \(n \leqslant 3\). Finally, we conclude that the tori, \(\mathbb {T}^1\), \(\mathbb {T}^2\) and \(\mathbb {T}^3\), are Wecken spaces in Nielsen–Borsuk–Ulam theory. Such a number is a lower bound for the minimal number of pair of points such that \(f(x)=f(\tau (x))\) in a given homotopy class of maps.
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The first author was supported by CAPES-Brazil, the second author was partially supported by FAPESP, Projeto Temático: Topologia Algébrica, Geométrica e Diferencial, 2016/24707-4.
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de Melo, G.D., Vendrúscolo, D. Nielsen–Borsuk–Ulam number for maps between tori. J. Fixed Point Theory Appl. 25, 61 (2023). https://doi.org/10.1007/s11784-023-01065-9
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DOI: https://doi.org/10.1007/s11784-023-01065-9