On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

TL;DR

This paper investigates the connectedness properties of the moduli space of flat G-connections on compact surfaces for various Lie groups, including simply connected and certain classical groups, enhancing understanding of their topological structure.

Contribution

It establishes the connectedness of the moduli space for a broad class of compact Lie groups, including non-semisimple and classical groups, extending previous results.

Findings

Connectedness of moduli space for simply connected Lie groups.

Connectedness results for U(n) and Spin^C(n).

Extension of known topological properties to non-semisimple groups.

Abstract

We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups including U(n) and Spin^C(n).