Aspects of the topology and combinatorics of Higgs bundle moduli spaces

TL;DR

This survey explores the topology and combinatorics of Higgs bundle moduli spaces on Riemann surfaces, highlighting how cohomology ring structures inspire combinatorial questions.

Contribution

It introduces fundamental questions and techniques related to the topology of Higgs bundle moduli spaces and illustrates their combinatorial aspects through examples.

Findings

Cohomology ring structures reveal combinatorial problems.

Examples demonstrate the interplay between topology and combinatorics.

The survey highlights open questions in the field.

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.