Non-trivial extensions in equivariant cohomology with constant coefficients

TL;DR

This paper advances the understanding of equivariant cohomology over cyclic groups of prime power order by providing new computational formulas and demonstrating the existence of non-trivial extensions in specific cases.

Contribution

It introduces an inductive formula for equivariant cohomology with constant coefficients and proves the existence of non-trivial extensions for groups of order at least $p^3$.

Findings

Inductive formula for equivariant cohomology when fixed points are large.

Existence of non-trivial extensions for $n \\geq 3$.

Computational results for cyclic groups of prime power order.

Abstract

In this paper, we prove some computational results about equivariant cohomology over the cyclic group $C_{p^n}$ of prime power order. We show that there is an inductive formula when the dimension of the $C_p$-fixed points of the grading is large. Among other calculations, we also show the existence of non-trivial extensions when $n\geq 3$.