Mapping class groups of medium distance Heegaard splittings
Geometric Topology
2009-10-28 v1
Abstract
We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that given two handlebody sets in the curve complex for a surface that are distance at least four apart, the group of automorphisms of the curve complex that preserve both handlebody sets is finite.
Cite
@article{arxiv.0910.5190,
title = {Mapping class groups of medium distance Heegaard splittings},
author = {Jesse Johnson},
journal= {arXiv preprint arXiv:0910.5190},
year = {2009}
}
Comments
9 pages, 1 figure