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

Autor:	Hazel, Christy
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Topology 55N91 55P91
Druh dokumentu:	Working Paper
Popis:	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 the action is orientation preserving versus reversing in the orientable case, and one other invariant. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.04656 Zobrazit plný text záznamu View this record from Arxiv