Mapping class groups of medium distance Heegaard splittings

Details Mapping class groups of medium distance Heegaard splittings Mapping class groups of medium distance Heegaard splittings

2009-10-27

arxiv.org/abs/0910.5190v1

Mathematics

Geometric Topology

9 pages, 1 figure

Scientific paper

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.

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