The Mapping Class Group acts reducibly on SU(n)-character varieties
| dc.creator | Goldman, William M. | |
| dc.date | 2005-09-06 | |
| dc.date | 2005-09-22 | |
| dc.date.accessioned | 2026-07-07T08:10:20Z | |
| dc.date.available | 2026-07-07T08:10:20Z | |
| dc.description | When $G$ is a connected compact Lie group, and $π$ is a closed surface group, then $Hom(π,G)$ contains an open dense $Out(π)$-invariant subset which is a smooth symplectic manifold. This symplectic structure is $Out(π)$-invariant and therefore defines an invariant measure $μ$, which has finite volume. The corresponding unitary representation of $Out(π)$ on $L^2(Hom(π,G)/G,μ)$ contains no finite-dimensional subrepresentations besides the constants. This note gives a short proof that when $G=SU(n)$, the representation $L^2(Hom(π,G)/G,μ)$ contains many other invariant subspaces. | |
| dc.description | 6 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0509115 | |
| dc.identifier | http://arxiv.org/abs/math/0509115 | |
| dc.identifier | Primes and knots, 115--119, Contemp. Math., 416, Amer. Math. Soc., Providence, RI, 2006. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131794 | |
| dc.subject | Geometric Topology | |
| dc.subject | 58E20, 57M30 | |
| dc.title | The Mapping Class Group acts reducibly on SU(n)-character varieties | |
| dc.type | text |