{"paper":{"title":"Moduli spaces of vector bundles with fixed determinant over a real curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Thomas John Baird","submitted_at":"2017-03-02T13:41:29Z","abstract_excerpt":"Let $(\\Sigma,\\tau)$ denote a Riemann surface of genus $g \\geq 2$ equipped with an anti-holomorphic involution $\\tau$. In this paper we study the topology of the moduli space $M(r,\\xi)^\\tau$ of stable Real vector bundles over $(\\Sigma,\\tau)$ of rank $r$ and fixed determinant $\\xi$ of degree coprime to $r$.\n  We prove that $M(r,\\xi)^{\\tau}$ is an orientable and monotone Lagrangian submanifold of the complex moduli space $M(r,\\xi)$ so it determines an object in the appropriate Fukaya category. We derive recursive formulas for the mod $2$ Betti numbers of $M(r,\\xi)^\\tau$ and compute mod $p$ Betti "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00778","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}