Some 3-manifolds and 3-orbifolds with large fundamental group
| dc.creator | Lackenby, Marc | |
| dc.date | 2005-07-14 | |
| dc.date.accessioned | 2026-07-07T05:21:41Z | |
| dc.date.available | 2026-07-07T05:21:41Z | |
| dc.description | We provide two new proofs of a theorem of Cooper, Long and Reid which asserts that, apart from an explicit finite list of exceptional manifolds, any compact orientable irreducible 3-manifold with non-empty boundary has large fundamental group. The first proof is direct and topological; the second is group-theoretic. These techniques are then applied to prove a string of results about (possibly closed) 3-orbifolds, which culminate in the following theorem. If K is a knot in a compact orientable 3-manifold M, such that the complement of K admits a finite-volume hyperbolic structure, then the orbifold obtained by assigning a singularity of order n along K has large fundamental group, for infinitely many positive integers n. We also obtain information about this set of values of n. When M is the 3-sphere, this has implications for the cyclic branched covers over the knot. In this case, we may also weaken the hypothesis that the complement of K is hyperbolic to the assumption that K is non-trivial. | |
| dc.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0507283 | |
| dc.identifier | http://arxiv.org/abs/math/0507283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75779 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10, 57M25 | |
| dc.title | Some 3-manifolds and 3-orbifolds with large fundamental group | |
| dc.type | text |