The Heegaard structure of Dehn filled manifolds

Details The Heegaard structure of Dehn filled manifolds The Heegaard structure of Dehn filled manifolds

2007-06-13

arxiv.org/abs/0706.1927v2

Geom. Topol. Monogr. 12 (2007) 233-263

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 3 December 2007

Scientific paper

10.2140/gtm.2007.12.233

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).

Affiliated with

Also associated with

No associations

Rating

The Heegaard structure of Dehn filled manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Heegaard structure of Dehn filled manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Heegaard structure of Dehn filled manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-451286