Spectral geometry, link complements and surgery diagrams
| dc.creator | Lackenby, Marc | |
| dc.date | 2008-10-29 | |
| dc.date.accessioned | 2026-07-07T10:13:53Z | |
| dc.date.available | 2026-07-07T10:13:53Z | |
| dc.description | We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of hyperbolic alternating link complements is expanding if and only if they have bounded volume. We also provide examples of hyperbolic 3-manifolds which require 'complicated' surgery diagrams, thereby proving that a recent theorem of Constantino and Thurston is sharp. Along the way, we find a new upper bound on the bridge number of a knot that is not tangle composite, in terms of the twist number of any diagram of the knot. The proofs rely on a theorem of Lipton and Tarjan on planar graphs, and also the relationship between many different notions of width for knots and 3-manifolds. | |
| dc.description | 20 pages, 11 figures | |
| dc.identifier | https://arxiv.org/abs/0810.5252 | |
| dc.identifier | http://arxiv.org/abs/0810.5252 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172690 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 57N10, 57M25, 58J50 | |
| dc.title | Spectral geometry, link complements and surgery diagrams | |
| dc.type | text |