Big Handlebody Distance Implies Finite Mapping Class Group

2004/06/27 by Hossein Namazi, Namazi, Hossein
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/0406551

9 pages

arxiv created 2004/06/29 · arxiv updated 2009/12/01

Abstract

We show that if M is a closed three manifold with a Heegaard splitting with sufficiently big "handlebody distance" then the subgroup of the mapping class group of the Heegaard surface, which extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of M is finite.

Related

• Mapping class groups of medium distance Heegaard splittings
• Finiteness of mapping class groups and Heegaard distance
• The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold
• High distance knots in closed 3-manifolds
• Quasi-homomorphisms on mapping class groups vanishing on a handlebody group