Uniqueness in Haken's Theorem

Fuente: arXiv
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Autores principales: Freedman, Michael, Scharlemann, Martin
Formato: Preprint
Publicado: 2020
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author Freedman, Michael
Scharlemann, Martin
author_facet Freedman, Michael
Scharlemann, Martin
contents Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isotoped so that it intersects E in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel E 2) pushing a stabilizing pair of T through E and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.
format Preprint
id arxiv_https___arxiv_org_abs_2004_07385
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Uniqueness in Haken's Theorem
Freedman, Michael
Scharlemann, Martin
Geometric Topology
57K35
Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isotoped so that it intersects E in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel E 2) pushing a stabilizing pair of T through E and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.
title Uniqueness in Haken's Theorem
topic Geometric Topology
57K35
url https://arxiv.org/abs/2004.07385