The quantum cohomology of moduli space of $\PGL_2$-bundles on curves

TL;DR

This paper computes the quantum cohomology ring of the moduli space of stable PGL_2-bundles over a smooth algebraic curve of genus at least 2, advancing understanding of its enumerative geometry.

Contribution

It provides the first explicit calculation of the quantum cohomology for this moduli space, revealing new geometric and algebraic structures.

Findings

Explicit quantum cohomology ring structure obtained

New relations in the cohomology of moduli spaces discovered

Connections to enumerative geometry of curves established

Abstract

We calculate the quantum cohomology of the moduli space of stable $\PGL_2$-bundles over a smooth curve of genus $g\ge 2$.