The Heegaard structure of Dehn filled manifolds
Abstract
Description
We expect manifolds obtained by Dehn filling to inherit properties from the knot manifold. To what extent does that hold true for the Heegaard structure? We study four changes to the Heegaard structure that may occur after filling: (1) Heegaard genus decreases, (2) a new Heegaard surface is created, (3) a non-stabilized Heegaard surface destabilizes, and (4) two or more non-isotopic Heegaard surfaces become isotopic. We survey general results that give quite satisfactory restrictions to phenomena (1) and (2) and, in a parallel thread, give a complete classification of when all four phenomena occur when filling most torus knot exteriors. This latter thread yields sufficient (and perhaps necessary) conditions for the occurrence of phenomena (3) and (4).
This is the version published by Geometry & Topology Monographs on 3 December 2007
This is the version published by Geometry & Topology Monographs on 3 December 2007