Connected Components of The Space of Surface Group Representations
| dc.creator | Ho, Nan-Kuo | |
| dc.creator | Liu, Chiu-Chu Melissa | |
| dc.date | 2003-03-20 | |
| dc.date.accessioned | 2026-07-07T04:56:14Z | |
| dc.date.available | 2026-07-07T04:56:14Z | |
| dc.description | Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $Σ$ of genus $l >1$, the order of the group $H^2(Σ,π_1(G))$ is equal to the number of connected components of the space $Hom(π_1(Σ),G)/G$ which can also be identified with the moduli space of gauge equivalence classes of flat G-bundles over $Σ$. We show that the same statement for a closed compact nonorientable surface which is homeomorphic to the connected sum of k copies of the real projective plane, where $k\neq 1,2,4$, can be easily derived from a result in A. Alekseev, A.Malkin and E. Meinrenken's recent work on Lie group valued moment maps. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303255 | |
| dc.identifier | http://arxiv.org/abs/math/0303255 | |
| dc.identifier | IMRN 2003, no.44, 2359-2372 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66848 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53D99 | |
| dc.title | Connected Components of The Space of Surface Group Representations | |
| dc.type | text |