Horizontal Dehn Surgery and genericity in the curve complex

Details Horizontal Dehn Surgery and genericity in the curve complex Horizontal Dehn Surgery and genericity in the curve complex

2007-11-28

arxiv.org/abs/0711.4492v4

Mathematics

Geometric Topology

This version contains a substantially stronger version of the main theorem. 31 pages 4 figures

Scientific paper

We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured laminations in S, equipped with its natural Lebesgue measure. We prove that, for any 3-manifold M, the set of curves c on a Heegaard surface S in M, such that every non-trivial Dehn twist at c yields a Heegaard splitting of high distance, is generic in the set of all essential simple closed curves on S. Our definition of "genericity" is different and more intrinsic than alternative such existing notions, given e.g. via random walks or via limits of quotients of finite sets.

Affiliated with

Also associated with

No associations

Rating

Horizontal Dehn Surgery and genericity in the curve complex 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 Horizontal Dehn Surgery and genericity in the curve complex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Horizontal Dehn Surgery and genericity in the curve complex will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-249494