2026-08-16T04:45:20Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/502002023-08-11T08:14:24Zcom_20.500.14352_14col_20.500.14352_15

Biswas, Indrani Muñoz, Vicente 2023-06-20T09:41:47Z 2023-06-20T09:41:47Z 2008 1019-8385 https://hdl.handle.net/20.500.14352/50200 http://www.intlpress.com/CAG/ http://www.intlpress.com We study the rational homotopy of the moduli space N-X that parametrizes the isomorphism classes of all stable vector bundles of rank two and fixed determinant of odd degree over a compact connected Riemann surface X of genus g, with g >= 2. The symplectic group Aut(H-1(X, Z)) congruent to Sp(2g, Z) has a natural action on the rational homotopy groups pi(n)(N-X)circle times(Z)Q. We prove that this action extends to an action of Sp(2g, C) on pi(n)(N-X)circle times C-Z. We also show that pi(n)(N-X)circle times C-Z is a non-trivial representation of Sp(2g, C) congruent to Aut (H-1(X, C)) for all n >= 2g - 1. In particular, N-X is a rationally hyperbolic space. In the special case where g = 2, for each n is an element of N, we compute the leading Sp(2g, C) representation occurring in pi(n)(N-X)circle times C-Z. eng restricted access On the rational homotopy type of a moduli space of vector bundles over a curve journal article