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arXiv · 1907.07280

The $RO(C_2)$-graded cohomology of $C_2$-surfaces in $\underline{\mathbb{Z}/2}$-coefficients

Christy Hazel
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Abstract

A surface with an involution can be viewed as a $C_2$-space where $C_2$ is the cyclic group of order two. Using the classification of $C_2$-surfaces given by Dugger, we compute the $RO(C_2)$-graded Bredon cohomology of all $C_2$-surfaces in constant $\mathbb{Z}/2$ coefficients as modules over the cohomology of a point. We show the cohomology depends only on three numerical invariants in the nonfree case, and only on two numerical invariants in the free case.

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Christy Hazel. 2019-07-16. The $RO(C_2)$-graded cohomology of $C_2$-surfaces in $\underline{\mathbb{Z}/2}$-coefficients. https://arxiv.org/abs/1907.07280

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