Equivariant instanton Floer homology and calculations for the binary polyhedral spaces

TL;DR

This paper computes the equivariant instanton Floer homology for binary polyhedral spaces, providing new algebraic modifications to the existing framework, with implications for understanding these 3-manifolds.

Contribution

It introduces a modified algebraic construction for equivariant instanton Floer homology and performs explicit calculations for binary polyhedral spaces.

Findings

Computed equivariant instanton Floer homology for binary polyhedral spaces

Modified algebraic structures in the Floer homology framework

Results applicable over rings where 2 is invertible

Abstract

We calculate the equivariant instanton Floer homology, in the sense of Miller Eismeier, for the trivial $SO(3)$-bundle over the binary polyhedral spaces with coefficients in a PID $R$ for which $2\in R$ is invertible. Along the way we modify a part of the algebraic construction needed to define the equivariant instanton Floer groups.