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Big Heegaard distance implies finite mapping class group

By Hossein Namazi


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

Topics: Key words, Heegaard splitting, Heegaard distance, curve complex
Year: 2013
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