Fiber respecting quasi-isometries of surface group extensions
| dc.creator | Mosher, Lee | |
| dc.date | 2003-08-07 | |
| dc.date.accessioned | 2026-07-07T05:00:13Z | |
| dc.date.available | 2026-07-07T05:00:13Z | |
| dc.description | Let S be a closed, oriented surface of genus at least 2, and consider the extension 1 -> pi_1 S -> MCG(S,p) -> MCG(S) -> 1, where MCG(S) is the mapping class group of S, and MCG(S,p) is the mapping class group of S punctured at p. We prove that any quasi-isometry of MCG(S,p) which coarsely respects the cosets of the normal subgroup pi_1 S is a bounded distance from the left action of some element of MCG(S,p). Combined with recent work of Kevin Whyte this implies that if K is a finitely generated group quasi-isometric to MCG(S,p) then there is a homomorphism K -> MCG(S,p) with finite kernel and finite index image. Our work applies as well to extensions of the form 1 -> pi_1 S -> Gamma_H -> H -> 1, where H is an irreducible subgroup of MCG(S)--we give an algebraic characterization of quasi-isometries of Gamma_H that coarsely respect cosets of pi_1 S. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308067 | |
| dc.identifier | http://arxiv.org/abs/math/0308067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68269 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.title | Fiber respecting quasi-isometries of surface group extensions | |
| dc.type | text |