Ubiquity of geometric finiteness in mapping class groups of Haken 3-manifolds
| dc.creator | Hong, Sungbok | |
| dc.creator | McCullough, Darryl | |
| dc.date | 1997-12-13 | |
| dc.date.accessioned | 2026-07-07T05:23:25Z | |
| dc.date.available | 2026-07-07T05:23:25Z | |
| dc.description | Mapping class groups of Haken 3-manifolds enjoy many of the homological finiteness properties of mapping class groups of 2-manifolds of finite type. For example, H(M) has a torsionfree subgroup of finite index, which is geometrically finite (i. e. is the fundamental group of a finite aspherical complex). This was proven by J. Harer for 2-manifolds and by the second author for Haken 3-manifolds. In this paper we prove that H(M) acts properly discontinuously on a contractible simplicial complex, with compact quotient. This implies that every torsionfree subgroup of finite index in H(M) is geometrically finite. Also, a simplified proof of the fact that torsionfree subgroups of finite index in H(M) exist is given. All results are proven for mapping class groups that preserve a boundary pattern in the sense of K. Johannson. As an application, we show that if F is a nonempty compact 2-manifold in the boundary of M, then the classifying space BDiff(M rel F) of the diffeomorphism group of M relative to F has the homotopy type of a finite aspherical complex. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/9712250 | |
| dc.identifier | http://arxiv.org/abs/math/9712250 | |
| dc.identifier | Pacific J. Math. 188 (1999), 275-301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76429 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | Ubiquity of geometric finiteness in mapping class groups of Haken 3-manifolds | |
| dc.type | text |