Stabilizing Heegaard splittings of toroidal 3-manifolds

dc.creatorDerby-Talbot, Ryan
dc.date2006-04-05
dc.date2007-04-29
dc.date.accessioned2026-07-07T07:58:29Z
dc.date.available2026-07-07T07:58:29Z
dc.descriptionLet $T$ be a separating incompressible torus in a 3-manifold $M$. Assuming that a genus $g$ Heegaard splitting $V \cup_S W$ can be positioned nicely with respect to $T$ (e.g. $V \cup_S W$ is strongly irreducible), we obtain an upper bound on the number of stabilizations required for $V \cup_S W$ to become isotopic to a Heegaard splitting which is an amalgamation along $T$. In particular, if $T$ is a canonical torus in the JSJ decomposition of $M$, then the number of necessary stabilizations is at most $4g-4$. As a corollary, this establishes an upper bound on the number of stabilizations required for $V \cup_S W$ and any Heegaard splitting obtained by a Dehn twist of $V \cup_S W$ along $T$ to become isotopic.
dc.description21 pages, 18 figures. Version for publication. Generalization of the main theorem and minor changes in style and format
dc.identifierhttps://arxiv.org/abs/math/0604115
dc.identifierhttp://arxiv.org/abs/math/0604115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128026
dc.subjectGeometric Topology
dc.subject57M99
dc.titleStabilizing Heegaard splittings of toroidal 3-manifolds
dc.typetext

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