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.

arXiv comment18 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

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Cited by in corpus (8)

• Stable maps to Looijenga pairs
• Moduli spaces of generalized hyperpolygons
• Non-Abelian Hodge Theory and Related Topics
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Nonabelian Hodge theory and vector valued modular forms
• Higgs bundles without geometry
• Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs
• Smoothness of non-reductive fixed point sets and cohomology of non-reductive GIT quotients