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arXiv · 2306.03948

The $RO(C_3)$-graded Bredon cohomology of $C_3$-surfaces in $\underline{\mathbb{Z}/3}$-coefficients

Kelly Pohland
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Abstract

Using an equivariant surgery classification, we compute the $RO(C_3)$-graded Bredon cohomology of all $C_3$-surfaces in constant $\mathbb{Z}/3$-coefficients as modules over the cohomology of a fixed point. We show that the cohomology of a given $C_3$-surface is determined by a handful of topological invariants and is directly determined by the construction of the surface via equivariant surgery.

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Kelly Pohland. 2023-06-06. The $RO(C_3)$-graded Bredon cohomology of $C_3$-surfaces in $\underline{\mathbb{Z}/3}$-coefficients. https://arxiv.org/abs/2306.03948

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