Moduli spaces of vector bundles over a real curve: Z/2-Betti numbers

TL;DR

This paper computes the Z/2-Betti numbers of moduli spaces of real vector bundles over real curves, using adapted Atiyah-Bott methods, confirming recent formulas by Liu and Schaffhauser.

Contribution

It adapts Atiyah-Bott techniques to real bundles, providing explicit Betti number formulas for these moduli spaces.

Findings

Computed Z/2-Betti numbers for real bundle moduli spaces

Confirmed recent formulas by Liu and Schaffhauser

Extended Atiyah-Bott methods to real algebraic geometry

Abstract

Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's "Yang-Mills over a Riemann Surface" to compute Z/2-Betti numbers of these spaces, proving formulas recently obtained by Liu and Schaffhauser.