Extension problem of subset-controlled quasimorphisms

Kawasaki, Morimichi

doi:10.1090/bproc/31

Extension problem of subset-controlled quasimorphisms
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Proc. Amer. Math. Soc. Ser. B 5 (2018), 1-5

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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