Cohomology of the Moduli Space of Rank Two, Odd Degree Vector Bundles over a Real Curve

TL;DR

This paper computes the singular cohomology ring of the moduli space of rank two, odd degree, semi-stable Real vector bundles over real curves, providing new insights into their topological structure.

Contribution

It presents the first detailed calculation of the cohomology ring for these moduli spaces in various characteristics, expanding understanding of their topology.

Findings

Cohomology ring computed for most examples in odd and zero characteristic.

Provides explicit descriptions of the cohomological structure.

Enhances understanding of the topology of moduli spaces of Real vector bundles.

Abstract

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.