Mapping class groups of medium distance Heegaard splittings

Jesse Johnson

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arXiv · 0910.5190

Mapping class groups of medium distance Heegaard splittings

Jesse Johnson

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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.

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Jesse Johnson. 2009-10-27. Mapping class groups of medium distance Heegaard splittings. https://arxiv.org/abs/0910.5190

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