Fundamental Groups of Character Varieties: Surfaces and Tori

TL;DR

This paper calculates the fundamental groups of moduli spaces of Lie group representations for surfaces and tori, providing insights into their topological structure.

Contribution

It introduces explicit computations of fundamental groups for these moduli spaces, advancing understanding of their topological properties.

Findings

Fundamental groups of surface representation moduli spaces determined

Fundamental groups of torus representation moduli spaces determined

New topological invariants for these moduli spaces identified

Abstract

We compute the fundamental group of moduli spaces of Lie group valued representations of surface and torus groups.