Length and stable length
| dc.creator | Calegari, Danny | |
| dc.date | 2006-05-15 | |
| dc.date | 2007-06-06 | |
| dc.date.accessioned | 2026-07-07T09:35:55Z | |
| dc.date.available | 2026-07-07T09:35:55Z | |
| dc.description | This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive e there is a positive d depending only on n and on e such that an element of pi_1(M) with stable commutator length less than d is represented by a geodesic with length less than e. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12. Conversely, "most" short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of homological Margulis constant. | |
| dc.description | 22 pages, 2 figures; version 4: incorporates referee's suggestions | |
| dc.identifier | https://arxiv.org/abs/math/0605354 | |
| dc.identifier | http://arxiv.org/abs/math/0605354 | |
| dc.identifier | Geom. Func. Anal. 18 (2008), no. 1, 50-76 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159996 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M50; 20F65 | |
| dc.title | Length and stable length | |
| dc.type | text |