Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 129, 18 pages      arXiv:1809.05732      https://doi.org/10.3842/SIGMA.2018.129
Contribution to the Special Issue on Geometry and Physics of Hitchin Systems

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

Received September 23, 2018, in final form December 04, 2018; Published online December 07, 2018

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.

Key words: Higgs bundle; Morse-Bott theory; localization; Betti number; moduli space; stability; quiver; partition problem.

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