Moduli of flat SU(3)-bundles over a Klein bottle

TL;DR

This paper computes the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle, confirming conjectures and extending results to general compact groups over RP^2, with implications for equivariant formality.

Contribution

It provides explicit Betti number calculations for these moduli stacks and verifies conjectural formulas, advancing understanding of their topological structure.

Findings

Betti numbers of moduli stacks computed

Cohomology found to be equivariantly formal

Conjectural formulas verified using Yang-Mills Morse theory

Abstract

In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal, supporting a conjecture from the author's doctoral thesis. Our results also verify conjectural formulas obtained by Ho-Liu using Yang-Mills Morse theory.