arXiv subjects

Kelly Pohland

Publications and source records attributed to Kelly Pohland.

2 recordsLinked to original sources

arXiv2023

An equivariant surgery classification of $C_p$-surfaces

Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We additionally provide a way to construct representatives of each isomorphism class using a series of equivariant surgery operations. The results in this paper serve as an odd prime analogue to a similar classification proved by Dan Dugger.

math.GT↗

arXiv2023

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

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.

math.AT↗