Incompressibility and normal minimal surfaces
| dc.creator | Kalelkar, Tejas | |
| dc.date | 2008-10-01 | |
| dc.date.accessioned | 2026-07-07T10:06:42Z | |
| dc.date.available | 2026-07-07T10:06:42Z | |
| dc.description | In this paper we describe a procedure for refining the given triangulation of a 3-manifold that scales the PL-metric according to a given weight function while creating no new normal surfaces. It is known that an incompressible surface $F$ in a triangulated 3-manifold $M$ is isotopic to a normal surface that is of minimal PL-area in the isotopy class of $F$. Using the above scaling refinement we prove the converse. If $F$ is a surface in a closed 3-manifold $M$ such that for any triangulation $τ$ of $M$, $F$ is isotopic to a $τ$-normal surface $F(τ)$ that is of minimal PL-area in its isotopy class, then we show that $F$ is incompressible. | |
| dc.description | 10 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0810.0187 | |
| dc.identifier | http://arxiv.org/abs/0810.0187 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170416 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57Q35 (Primary), 57M99 (Secondary) | |
| dc.title | Incompressibility and normal minimal surfaces | |
| dc.type | text |