Biswas, IndraniMuñoz, Vicente2023-06-202023-06-2020081019-8385https://hdl.handle.net/20.500.14352/50200We 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.engjournal articlehttp://www.intlpress.com/CAG/http://www.intlpress.comrestricted access512.7514Vector bundlesModuli spaceSmooth projective curveRiemann surfaceRational homotopy groupsGeometria algebraicaTopología1201.01 Geometría Algebraica1210 Topología