On real moduli spaces over M-curves

Abstract

Let $F$ be a genus $g$ curve and $\sigma :F\to F$ a real structure with the maximal possible number of fixed circles. We study the real moduli space $\N' = \Fix (σ^{#})$ where $σ^{#}: \N \to \N$ is the induced real structure on the moduli space $\mathbb{N}$ of stable holomorphic bundles of rank 2 over $F$ with fixed non-trivial determinant. In particular, we calculate $H^{\ast }({\mathbb{N}}^{\prime },\mathbb{Z})$ in the case of $g=2$, generalizing Thaddeus' approach to computing $H^{\ast }(\mathbb{N},\mathbb{Z})$.

13 pages, 2 figures