Components of spaces of representations and stable triples
| dc.creator | Gothen, Peter B. | |
| dc.date | 1999-04-21 | |
| dc.date | 2000-04-19 | |
| dc.date.accessioned | 2026-07-07T05:28:46Z | |
| dc.date.available | 2026-07-07T05:28:46Z | |
| dc.description | We consider the moduli spaces of representations of the fundamental group of a surface of genus g greater than 2 in the Lie groups SU(2,2) and Sp(4,R). It is well known that there is a characteristic number of such a representation, whose absolute value is less than or equal to 2g-2. This allows one to write the moduli space as a union of subspaces indexed by the characteristic number, each of which is a union of connected components. The main result of this paper is that the subspaces with characteristic number plus or minus 2g-2 are connected in the case of representations in SU(2,2), while they break up into 2^{2g+1}+2g-3 connected components in the case of representations in Sp(4,R). We obtain our results using the interpretation of the moduli space of representations as a moduli space of Higgs bundles, and an important step is an identification of certain subspaces as moduli spaces of stable triples, as studied by Bradlow and Garcia-Prada. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/9904114 | |
| dc.identifier | http://arxiv.org/abs/math/9904114 | |
| dc.identifier | Topology 40 (2001), 823-850 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78386 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20 | |
| dc.title | Components of spaces of representations and stable triples | |
| dc.type | text |