This article is cited in 9 papers

Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces

Steven Rayan

Department of Mathematics & Statistics, McLean Hall, University of Saskatchewan, Saskatoon, SK, Canada S7N 5E6

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.

Keywords: Higgs bundle; Morse–Bott theory; localization; Betti number; moduli space; stability; quiver; partition problem.

MSC: 14D20; 46M20; 57N65; 05A19

Received: September 23, 2018; in final form December 4, 2018; Published online December 7, 2018

Language: English

DOI: 10.3842/SIGMA.2018.129

Bibliographic databases:

• 
• 

ArXiv: 1809.05732