On the rational homotopy type of a moduli space of vector bundles over a curve
| dc.creator | Biswas, Indranil | |
| dc.creator | Muñoz, Vicente | |
| dc.date | 2006-05-19 | |
| dc.date | 2007-10-23 | |
| dc.date.accessioned | 2026-07-07T08:37:49Z | |
| dc.date.available | 2026-07-07T08:37:49Z | |
| dc.description | We study the rational homotopy of the moduli space ${\mathcal N}_X$ of stable vector bundles of rank two and fixed determinant of odd degree over a compact connected Riemann surface $X$ of genus $g\geq 2$. The symplectic group $Aut(H_1(X,{\mathbb Z}))=Sp(2g,{\mathbb Z})$ has a natural action on the rational homotopy groups $π_n({\mathcal N}_X) \otimes {\mathbb Q}$. We prove that this action extends to an action of $Sp(2g,{\mathbb C})$ on $π_n({\mathcal N}_X) \otimes {\mathbb C}$. We also show that $π_n({\mathcal N}_X) \otimes {\mathbb C}$ is a non-trivial $Sp(2g,{\mathbb C})$-representation for each $n\geq 2g-1$. In particular, ${\mathcal N}_X$ is a rationally hyperbolic space. In the special case where $g=2$, we compute the leading $Sp(2g,{\mathbb C})$-representation occurring in $π_n({\mathcal N}_X) \otimes {\mathbb C}$, for each $n$. | |
| dc.description | 27 pages, no figures; v2. final version. To appear in Comm. Analysis and Geom | |
| dc.identifier | https://arxiv.org/abs/math/0605542 | |
| dc.identifier | http://arxiv.org/abs/math/0605542 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140536 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 14H60; 55P62 | |
| dc.title | On the rational homotopy type of a moduli space of vector bundles over a curve | |
| dc.type | text |