Abstract:The algebraic cobordism spectra $\mathbf {MSL}$ and $\mathbf {MSp}$ are constructed. They are commutative monoids in the category of symmetric $T^{\wedge 2}$-spectra. The spectrum $\mathbf {MSp}$ comes with a natural symplectic orientation given either by a tautological Thom class $th^{\mathbf {MSp}} \in \mathbf {MSp}^{4,2}(\mathbf {MSp}_2)$, or a tautological Borel class $b_{1}^{\mathbf {MSp}} \in \mathbf {MSp}^{4,2}(HP^{\infty })$, or any of six other equivalent structures. For a commutative monoid $E$ in the category ${SH}(S)$, it is proved that the assignment $\varphi \mapsto \varphi (th^{\mathbf {MSp}})$ identifies the set of homomorphisms of monoids $\varphi \colon \mathbf {MSp}\to E$ in the motivic stable homotopy category $SH(S)$ with the set of tautological Thom elements of symplectic orientations of $E$. A weaker universality result is obtained for $\mathbf {MSL}$ and special linear orientations. The universality of $\mathbf {MSp}$ has been used by the authors to prove a Conner–Floyed type theorem. The weak universality of $\mathbf {MSL}$ has been used by A. Ananyevskiy to prove another version of the Conner–Floyed type theorem.

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中文翻译：

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关于代数余谱 𝐌𝐒𝐋 和 𝐌𝐒𝐩

摘要:构造了代数余谱$\mathbf {MSL}$和$\mathbf {MSp}$。它们是对称 $T^{\wedge 2}$-谱类别中的可交换幺半群。谱 $\mathbf {MSp}$ 带有一个自然的辛方向，由重言式 Thom 类 $th^{\mathbf {MSp}} \in \mathbf {MSp}^{4,2}(\mathbf {MSp }_2)$，或重言式 Borel 类 $b_{1}^{\mathbf {MSp}} \in \mathbf {MSp}^{4,2}(HP^{\infty })$，或六个中的任何一个其他等效结构。对于类别 ${SH}(S)$ 中的交换幺半群 $E$，证明赋值 $\varphi \mapsto \varphi (th^{\mathbf {MSp}})$ 标识了同态集合动力稳定同伦范畴 $SH(S)$ 中的幺半群 $\varphi \colon \mathbf {MSp}\to E$ 与辛取向为 $E$ 的重言式 Thom 元素集。对于 $\mathbf {MSL}$ 和特殊的线性方向，获得了较弱的普适性结果。$\mathbf {MSp}$ 的普遍性已被作者用来证明 Conner–Floyed 类型定理。$\mathbf {MSL}$ 的弱普遍性已被 A. Ananyevskiy 用来证明康纳-弗洛伊德类型定理的另一个版本。

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