The moduli space of stable vector bundles over a real algebraic curve

TL;DR

This paper investigates the structure and topological invariants of moduli spaces of stable real and quaternionic vector bundles on real algebraic curves, linking them to unitary representations and connections.

Contribution

It establishes a relationship between these moduli spaces and unitary representations of an extension of the fundamental group, and computes their basic topological invariants.

Findings

Relationship with unitary representations of an extension of the fundamental group

Calculation of basic topological invariants of the moduli spaces

Comparison with the space of real or quaternionic connections

Abstract

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.