A proof of Waldhausen's uniqueness of splittings of S^3 (after Rubinstein and Scharlemann)
| dc.creator | Rieck, Yo'av | |
| dc.date | 2006-07-14 | |
| dc.date | 2009-03-31 | |
| dc.date.accessioned | 2026-07-07T12:58:16Z | |
| dc.date.available | 2026-07-07T12:58:16Z | |
| dc.description | In [Topology 35 (1996) 1005--1023] J H Rubinstein and M Scharlemann, using Cerf Theory, developed tools for comparing Heegaard splittings of irreducible, non-Haken manifolds. As a corollary of their work they obtained a new proof of Waldhausen's uniqueness of Heegaard splittings of S^3. In this note we use Cerf Theory and develop the tools needed for comparing Heegaard splittings of S^3. This allows us to use Rubinstein and Scharlemann's philosophy and obtain a simpler proof of Waldhausen's Theorem. The combinatorics we use are very similar to the game Hex and requires that Hex has a winner. The paper includes a proof of that fact (Proposition 3.6). | |
| dc.description | This is the version published by Geometry & Topology Monographs on 3 December 2007 | |
| dc.identifier | https://arxiv.org/abs/math/0607332 | |
| dc.identifier | http://arxiv.org/abs/math/0607332 | |
| dc.identifier | Geom. Topol. Monogr. 12 (2007) 277-284 | |
| dc.identifier | doi:10.2140/gtm.2007.12.277 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225184 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57M99 | |
| dc.title | A proof of Waldhausen's uniqueness of splittings of S^3 (after Rubinstein and Scharlemann) | |
| dc.type | text |