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

 

Realization of the mapping class group of handlebody by diffeomorphisms


Author: Susumu Hirose
Journal: Proc. Amer. Math. Soc. 138 (2010), 4157-4159
MSC (2010): Primary 57M60, 57N10
Published electronically: May 27, 2010
MathSciNet review: 2679638
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Abstract: For the oriented 3-dimensional handlebody constructed from a 3-ball by attaching $ g$ 1-handles, it is shown that the natural surjection from the group of orientation-preserving diffeomorphisms of it to the mapping class group of it has no section when $ g$ is at least 6.


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Additional Information

Susumu Hirose
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Saga University, Saga, 840–8502 Japan
Email: hirose@ms.saga-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10432-X
PII: S 0002-9939(2010)10432-X
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: February 5, 2010
Published electronically: May 27, 2010
Additional Notes: This research was supported by Grant-in-Aid for Scientific Research (C) (No. 20540083), Japan Society for the Promotion of Science.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.