Aspects of the topology and combinatorics of Higgs bundle moduli spaces

Abstract

This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space leads to interesting questions of a combinatorial nature.

18 pages; based on an invited mini-course given by the author at the University of Illinois at Chicago in October 2016; published in SIGMA Special Issue on Geometry and Physics of Hitchin Systems