Chen--Ruan cohomology of some moduli spaces

TL;DR

This paper computes the Chen--Ruan cohomology ring of a specific moduli space of stable PSL(2,C)-bundles over a compact Riemann surface of genus at least two, advancing understanding of orbifold cohomology in algebraic geometry.

Contribution

It provides the first explicit computation of Chen--Ruan cohomology for this class of moduli spaces, revealing new algebraic structures.

Findings

Explicit cohomology ring structure obtained

Identification of orbifold cohomology classes

Insights into the topology of moduli spaces

Abstract

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen--Ruan cohomology ring of the moduli space of stable PSL(2, C)--bundles of nontrivial second Stiefel--Whitney class over X.