Representations of surface groups and Higgs bundles

TL;DR

This paper introduces Higgs bundles and explores their role in understanding character varieties associated with surface group representations, providing foundational insights into their mathematical structure.

Contribution

It offers an accessible introduction to Higgs bundles and demonstrates their application to the study of surface group character varieties.

Findings

Higgs bundles provide a powerful framework for analyzing surface group representations.

The notes connect geometric structures with algebraic moduli spaces.

Foundational concepts for further research in surface group representations and Higgs bundle theory.

Abstract

These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group representations.