Critical Heegaard Surfaces
| dc.creator | Bachman, David | |
| dc.date | 2002-01-22 | |
| dc.date.accessioned | 2026-07-07T04:46:01Z | |
| dc.date.available | 2026-07-07T04:46:01Z | |
| dc.description | In this paper we introduce "critical surfaces", which are described via a 1-complex whose definition is reminiscent of the curve complex. Our main result is that if the minimal genus common stabilization of a pair of strongly irreducible Heegaard splittings of a 3-manifold is not critical, then the manifold contains an incompressible surface. Conversely, we also show that if a non-Haken 3-manifold admits at most one Heegaard splitting of each genus, then it does not contain a critical Heegaard surface. In the final section we discuss how this work leads to a natural metric on the space of strongly irreducible Heegaard splittings, as well as many new and interesting open questions. | |
| dc.description | 28 pages, 8 figures, to appear in Transactions of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/0201203 | |
| dc.identifier | http://arxiv.org/abs/math/0201203 | |
| dc.identifier | Transactions of the American Mathematical Society 354 (2002), 4015-4042. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63170 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | Critical Heegaard Surfaces | |
| dc.type | text |