Explicit Poincar\'e duality in the cohomology ring of the SU(2) character variety of a surface

TL;DR

This paper explicitly describes the Poincaré duals of generators in the rational cohomology ring of the SU(2) character variety of a surface, linking it to moduli spaces of stable bundles.

Contribution

It provides an explicit description of Poincaré duals in the cohomology ring of the SU(2) character variety, enhancing understanding of its topological structure.

Findings

Explicit formulas for Poincaré duals of generators

Connection between character varieties and moduli spaces

Advancement in understanding cohomology ring structure

Abstract

We provide an explicit description of the Poincar\'e dual of each generator of the rational cohomology ring of the $SU(2)$ character variety for a genus $g$ surface with central extension -- equivalently, that of the moduli space of stable holomorphic bundles of rank 2 and odd degree.