Gromov-Witten invariants of the moduli of bundles on a surface

1999/10/20 by Vicente Muñoz, Muñoz, Vicente
Mathematics · #14D20 #57R57 #58D27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:14D20 #msc:57R57 #msc:58D27

paper · pdf · doi:10.48550/arxiv.math/9910105

14 pages, no figures

arxiv created 1999/10/20 · openalex publication_date 1999/10/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We produce an equality between the Gromov-Witten invariants of the moduli space M of rank two odd degree stable vector bundles over a Riemann surface Σ and the Donaldson invariants of the algebraic surface Σ× P¹. We discuss on to how extent the Quantum cohomology of M determines its Gromow-Witten invariants. Finally we find the isomorphism between the usual cohomology and the Quantum cohomology for the moduli space M over a Riemann surface of genus g=3.

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