Homotopy types of gauge groups over Riemann surfaces

TL;DR

This paper investigates the homotopy types of gauge groups over Riemann surfaces for certain Lie groups, providing insights into the topology of moduli spaces of vector bundles.

Contribution

It offers a detailed analysis of gauge group homotopy types for principal G-bundles over Riemann surfaces, with applications to moduli space computations.

Findings

Homotopy types of gauge groups characterized for specific Lie groups.

Explicit calculations of homotopy groups of moduli spaces.

Connections established between gauge groups and vector bundle moduli spaces.

Abstract

Let $G$ be a compact connected Lie group with $\pi_1(G)\cong\mathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of the moduli spaces of stable vector bundles over Riemann surfaces.