The RO(C₃)-graded Bredon cohomology of C₃-surfaces in \underlineℤ/3-coefficients

2023/06/06 by Pohland, Kelly
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.03948

Abstract

Using an equivariant surgery classification, we compute the RO(C₃)-graded Bredon cohomology of all C₃-surfaces in constant ℤ/3-coefficients as modules over the cohomology of a fixed point. We show that the cohomology of a given C₃-surface is determined by a handful of topological invariants and is directly determined by the construction of the surface via equivariant surgery.

Related

• The RO(C₂)-graded cohomology of C₂-surfaces in\n underline\ℤ/2-coefficients
• Characterizing maximal varieties via Bredon cohomology
• Equivariant local coefficients and the RO(G)-graded cohomology of classifying spaces
• Computations in C_pq-Bredon cohomology
• The cohomology of C₂-surfaces with \underlineℤ-coefficients