## Abstract

Let script N_{g} be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree over a smooth complex projective curve of genus g. This paper gives a complete and very simple description of the rational cohomology ring H*(script N_{g}). A structural formula is proved for H*(script N_{g}), which was originally conjectured by Mumford. It is shown that the first relation in genus g between the standard generators satisfies a recurrence relation, first found by Zagier, and that the invariant subring for the mapping class group is a complete intersection ring. A Gröbner basis is found for the ideal of invariant relations; this leads to a natural monomial basis for H*(script N_{g}).

Original language | English |
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Pages (from-to) | 407-418 |

Number of pages | 12 |

Journal | Topology |

Volume | 37 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1998 |

## ASJC Scopus subject areas

- Geometry and Topology