Homology computation for a class of contact structures on $T^3$ and equivariant reductions

TL;DR

This paper computes the relative Contact Homology for a family of tight contact structures on the 3-torus using variational methods and explores algebraic equivariant homology reductions.

Contribution

It introduces a novel approach to computing contact homology for specific contact structures on the 3-torus and demonstrates algebraic equivariant reductions.

Findings

Computed relative Contact Homology for tight contact structures on T^3

Applied variational theory of critical points at infinity

Showed algebraic equivariant homology reductions

Abstract

We consider a family of tight contact structures on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show some algebraic equivariant homology reductions.