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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mapping class groups of medium distance Heegaard splittings


Author: Jesse Johnson
Journal: Proc. Amer. Math. Soc. 138 (2010), 4529-4535
MSC (2010): Primary 57Mxx
Published electronically: July 20, 2010
MathSciNet review: 2680077
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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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Additional Information

Jesse Johnson
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: jjohnson@math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10545-2
PII: S 0002-9939(2010)10545-2
Keywords: Heegaard splitting, mapping class group, curve complex
Received by editor(s): November 16, 2009
Published electronically: July 20, 2010
Additional Notes: This research was supported by NSF MSPRF grant 0602368
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.