Stabilizations of Heegaard splittings of sufficiently complicated 3-manifolds (Preliminary Report)
| dc.creator | Bachman, David | |
| dc.date | 2008-06-28 | |
| dc.date.accessioned | 2026-07-07T09:47:22Z | |
| dc.date.available | 2026-07-07T09:47:22Z | |
| dc.description | We construct families of manifolds that have pairs of genus $g$ Heegaard splittings that must be stabilized roughly $g$ times to become equivalent. We also show that when two unstabilized, boundary-unstabilized Heegaard splittings are amalgamated by a "sufficiently complicated" map, the resulting splitting is unstabilized. As a corollary, we produce a manifold that has distance one Heegaard splittings of arbitrarily high genus. Finally, we show that in a 3-manifold formed by a sufficiently complicated gluing, a low genus, unstabilized Heegaard splitting can be expressed in a unique way as an amalgamation over the gluing surface. | |
| dc.description | 10 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0806.4689 | |
| dc.identifier | http://arxiv.org/abs/0806.4689 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163849 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | Stabilizations of Heegaard splittings of sufficiently complicated 3-manifolds (Preliminary Report) | |
| dc.type | text |