The space of Heegaard Splittings

Details The space of Heegaard Splittings The space of Heegaard Splittings

2010-11-02

arxiv.org/abs/1011.0702v2

Mathematics

Geometric Topology

Minor rewriting as suggested by referee, no change in mathematical content. To appear in J. Reine Angew. Math

Scientific paper

For a Heegaard surface F in a closed orientable 3-manifold M, H(M,F) = Diff(M)/Diff(M,F) is the space of Heegaard surfaces equivalent to the Heegaard splitting (M,F). Its path components are the isotopy classes of Heegaard splittings equivalent to (M,F). We describe H(M,F) in terms of Diff(M) and the Goeritz group of (M,F). In particular, for hyperbolic M each path component is a classifying space for the Goeritz group, and when the (Hempel) distance of (M,F) is greater than 3, each path component of H(M,F) is contractible. For splittings of genus 0 or 1, we determine the complete homotopy type (modulo the Smale Conjecture for M in the cases when it is not known).

Affiliated with

Also associated with

No associations

Rating

The space of Heegaard Splittings 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 space of Heegaard Splittings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The space of Heegaard Splittings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-596000