Mapping class groups of medium distance Heegaard splittings

2009/10/27 by Jesse Johnson, Johnson, Jesse
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M

paper · pdf · doi:10.48550/arxiv.0910.5190

9 pages, 1 figure

arxiv created 2009/10/27 · arxiv updated 2009/12/01

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.

Related

• Big Handlebody Distance Implies Finite Mapping Class Group
• Mapping class groups of Heegaard splittings
• The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold
• High distance knots in closed 3-manifolds
• Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions