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Mapping class groups of medium distance Heegaard splittings
Author(s):
Jesse
Johnson
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4529-4535.
MSC (2010):
Primary 57Mxx
Posted:
July 20, 2010
MathSciNet review:
2680077
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Additional information
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:
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
Posted:
July 20, 2010
Additional Notes:
This research was supported by NSF MSPRF grant 0602368
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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