RT Journal Article
T1 On the rational homotopy type of a moduli space of vector bundles over a curve
A1 Biswas, Indrani
A1 Muñoz, Vicente
AB 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.
PB Int press co ltd
SN 1019-8385
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50200
UL https://hdl.handle.net/20.500.14352/50200
LA eng
NO MCyT
DS Docta Complutense
RD 4 abr 2025