Seiberg-Witten theory on finite covering spaces of spin 4-manifolds

TL;DR

This paper extends the computation of equivariant Bauer-Furuta degrees for spin 4-manifolds under finite group actions, covering cases with odd prime order groups using a representation-theoretic approach.

Contribution

It provides a new formula for the equivariant Bauer-Furuta degree for finite groups of odd prime order acting on spin 4-manifolds, complementing previous results for cyclic groups of order power of two.

Findings

Derived a formula for the degree when the group order is an odd prime

Extended the equivariant Bauer-Furuta degree computation to new group actions

Applied representation theory to finite dimensional approximations

Abstract

We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formula and its applications. We have treated the case when the group has order of odd degree. In particular we gave a formula of the degree when the order is odd-prime. Our approach is to use a representation-theoretic method on finite dimensional approximations of the functional spaces.