$C_2$ -曲面与${\underline{{\mathbb {Z}}}}$ -系数的上同调

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-01-20 DOI:10.1007/s40062-022-00321-y

Christy Hazel

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引用次数: 0

摘要

设$C_2$表示2阶的循环群。我们计算了所有具有常积分系数的$C_2$ -曲面的$RO(C_2)$ -梯度上同调。我们证明了当作用是非自由时，答案仅取决于格，下表面的可定向性，孤立不动点的数量，具有平凡法向束的固定圆的数量，以及具有非平凡法向束的固定圆的数量。当表面上的作用是自由的，我们证明了答案仅取决于格，下表面的定向性，作用是否保持定向，以及另一个不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$The cohomology of $C_2$-surfaces with ${\underline{{\mathbb {Z}}}}$-coefficients$

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The cohomology of $C_2$-surfaces with ${\underline{{\mathbb {Z}}}}$-coefficients

Let $C_2$ denote the cyclic group of order 2. We compute the $RO(C_2)$-graded cohomology of all $C_2$-surfaces with constant integral coefficients. We show when the action is nonfree, the answer depends only on the genus, the orientability of the underlying surface, the number of isolated fixed points, the number of fixed circles with trivial normal bundles, and the number of fixed circles with nontrivial normal bundles. When the action on the surface is free, we show the answer depends only on the genus, the orientability of the underlying surface, whether or not the action preserves the orientation, and one other invariant.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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发文量

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

\(C_2\) -曲面与\({\underline{{\mathbb {Z}}}}\) -系数的上同调

摘要