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Failure of separation by quasi-homomorphisms in mapping class groups
Author(s):
H.
Endo;
D.
Kotschick
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2747-2750.
MSC (2000):
Primary 20F65;
Secondary 20F12, 20F69, 57M07
Posted:
May 9, 2007
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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:
10.1090/S0002-9939-07-08866-1
PII:
S 0002-9939(07)08866-1
Received by editor(s):
June 8, 2006
Posted:
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 {\it Deutsche Forschungsgemeinschaft} and from JSPS Grant 18540083 is gratefully acknowledged
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2007,
American Mathematical Society
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