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

 

Failure of separation by quasi-homomorphisms in mapping class groups


Authors: H. Endo and D. Kotschick
Journal: Proc. Amer. Math. Soc. 135 (2007), 2747-2750
MSC (2000): Primary 20F65; Secondary 20F12, 20F69, 57M07
Published electronically: May 9, 2007
MathSciNet review: 2317948
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Abstract: We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous quasi-homomorphism vanishes on such an element, showing that elements of infinite order not conjugate to their inverses cannot be separated by quasi-homomorphisms.


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Additional Information

H. Endo
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: endo@math.wani.osaka-u.ac.jp

D. Kotschick
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, 80333 München, Germany
Email: dieter@member.ams.org

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08866-1
PII: S 0002-9939(07)08866-1
Received by editor(s): June 8, 2006
Published electronically: May 9, 2007
Additional Notes: The second author would like to thank L. Polterovich for a conversation raising the question whether a separation theorem for mapping class groups of higher genus surfaces holds, and K. Fujiwara and J. McCarthy for useful comments. Support from the Deutsche Forschungsgemeinschaft and from JSPS Grant 18540083 is gratefully acknowledged
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2007 American Mathematical Society