On contact modulo p L-space covers

TL;DR

This paper extends results on equivariant contact structures from minimal L-spaces to mod p L-spaces using Borel Floer cohomology and introduces new invariants related to group cohomology.

Contribution

It generalizes previous work to mod p L-spaces and introduces two new numerical invariants of equivariant contact structures.

Findings

Extension of results to mod p L-spaces.

Introduction of two new invariants.

Application of Serre spectral sequence in Borel Floer cohomology.

Abstract

The purpose of this article is to extend certain results of Roso (2023) which concerned equivariant contact structures on minimal L-spaces to the more general setting of mod p L-spaces. This is achieved by considering the Serre spectral sequence of the Borel Floer cohomology as showcased in Baraglia & Hekmati (2021). Along the way, the author introduces two new numerical invariants of equivariant contact structures which emerge from the structure of the Borel Floer cohomology as a module over the group cohomology.