Mapping class groups of compression bodies and 3-manifolds
| dc.creator | Oertel, Ulrich | |
| dc.date | 2006-07-18 | |
| dc.date | 2007-07-16 | |
| dc.date.accessioned | 2026-07-07T08:18:17Z | |
| dc.date.available | 2026-07-07T08:18:17Z | |
| dc.description | We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as automorphisms of (Q,V) rel V are called discrepant automorphisms, forming the mapping class group of discrepant automorphisms of W in Q. We describe a short exact sequence of these mapping class groups. For an orientable, compact, reducible 3 manifold W, there is a canonical "maximal" 4-dimensional compression body Q whose exterior boundary is W and whose interior boundary is the disjoint union of the irreducible summands of W. We obtain a short exact sequence for the mapping class group of a 3-manifold, which gives the mapping class group of the disjoint union of irreducible summands as a quotient of the entire mapping class group by the group of adjusting automorphisms. The group of discrepant automorphisms is described in terms of generators. The results are useful in a program for classifying automorphisms of compact 3-manifolds in the spirit of Nielsen-Thurston. | |
| dc.description | One fundamental error corrected. (Lemma 1.4, now Theorem 1.4.) 20 pages, 2 eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0607444 | |
| dc.identifier | http://arxiv.org/abs/math/0607444 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134380 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10; 57M99 | |
| dc.title | Mapping class groups of compression bodies and 3-manifolds | |
| dc.type | text |