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Quasi-morphisms on the group of area-preserving diffeomorphisms of the $ 2$-disk via braid groups


Author: Tomohiko Ishida
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 43-51
MSC (2010): Primary 37C15; Secondary 37E30
DOI: https://doi.org/10.1090/S2330-1511-2014-00002-X
Published electronically: March 25, 2014
MathSciNet review: 3181631
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Abstract: Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group $ {\rm Diff}_\Omega ^\infty (D^2, \partial D^2)$ of area-preserving diffeomorphisms of the $ 2$-disk $ D^2$. For the proof, they constructed a homomorphism from the space of quasi-morphisms on the braid group to the space of quasi-morphisms on $ {\rm Diff}_\Omega ^\infty (D^2, \partial D^2)$. In this paper, we study this homomorphism and prove its injectivity.


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Additional Information

Tomohiko Ishida
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Address at time of publication: Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
Email: ishidat@ms.u-tokyo.ac.jp, ishidat@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S2330-1511-2014-00002-X
Keywords: Area-preserving diffeomorphisms, symplectomorphisms, quasi-morphisms, pseudo-characters
Received by editor(s): July 19, 2012
Received by editor(s) in revised form: September 22, 2012, October 15, 2012, October 19, 2012, December 31, 2012, and February 27, 2013
Published electronically: March 25, 2014
Communicated by: Michael Wolf
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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