Topic
Surface subgroup conjecture
About: Surface subgroup conjecture is a research topic. Over the lifetime, 3 publications have been published within this topic receiving 14 citations.
Papers
Posted Content•
TL;DR: In this paper, it was shown that locally-isometric covers S'_i of S_i (for i = 1,2) can be obtained such that there is a (1+επsilon) bi-Lipschitz homeomorphism between S' i and S' ii and both locally isometric covers have bounded injectivity radius.
Abstract: We prove the following: 1. Let epsilon>0 and let S_1,S_2 be two closed
hyperbolic surfaces. Then there exists locally-isometric covers S'_i of S_i (for i=1,2)
such that there is a (1+\epsilon) bi-Lipschitz homeomorphism between S'_1 and S'_2 and both
covers S'_i have bounded injectivity radius. 2. Let M be a closed hyperbolic 3-manifold.
Then there exists a map j: S -> M where S is a surface of bounded injectivity radius and
j is a pi_1-injective local isometry onto its image.
12 citations
Posted Content•
TL;DR: This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by as discussed by the authors, which was later used by the authors of this paper, as well.
Abstract: This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic.
3 citations
Posted Content•
30 Nov 2004
TL;DR: In this paper, it was shown that there is a bi-Lipschitz homeomorphism between two closed hyperbolic surfaces with bounded injectivity radius and a locally-isometric cover.
Abstract: We prove the following: 1. Let epsilon>0 and let S_1,S_2 be two closed hyperbolic surfaces. Then there exists locally-isometric covers S'_i of S_i (for i=1,2) such that there is a (1+\epsilon) bi-Lipschitz homeomorphism between S'_1 and S'_2 and both covers S'_i have bounded injectivity radius. 2. Let M be a closed hyperbolic 3-manifold. Then there exists a map j: S -> M where S is a surface of bounded injectivity radius and j is a pi_1-injective local isometry onto its image.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2012 | 1 |
| 2004 | 2 |