Big Handlebody Distance Implies Finite Mapping Class Group

Details Big Handlebody Distance Implies Finite Mapping Class Group Big Handlebody Distance Implies Finite Mapping Class Group

2004-06-27

arxiv.org/abs/math/0406551v3

Mathematics

Geometric Topology

9 pages

Scientific paper

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.

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