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Proceedings of the American Mathematical Society Series B

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Extension problem of subset-controlled quasimorphisms


Author: Morimichi Kawasaki
Journal: Proc. Amer. Math. Soc. Ser. B 5 (2018), 1-5
MSC (2010): Primary 20J06, 53D22; Secondary 57M27
DOI: https://doi.org/10.1090/bproc/31
Published electronically: January 22, 2018
MathSciNet review: 3748593
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Abstract: Let $(G,H)$ be $(\mathrm {Ham}(\mathbb {R}^{2n}),\mathrm {Ham}(\mathbb {B}^{2n}))$ or $(B_\infty ,B_n)$. We conjecture that any semi-homogeneous subset-controlled quasimorphism on $[G,G]$ can be extended to a homogeneous subset-controlled quasimorphism on $G$ and also give a theorem supporting this conjecture by using a Bavard-type duality theorem on conjugation invariant norms.


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Additional Information

Morimichi Kawasaki
Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
Email: kawasaki@ibs.re.kr

Received by editor(s): December 18, 2016
Received by editor(s) in revised form: April 19, 2017, and September 1, 2017
Published electronically: January 22, 2018
Additional Notes: This work was supported by IBS-R003-D1.
Communicated by: Ken Bromberg
Article copyright: © Copyright 2018 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)