Extension problem of subset-controlled quasimorphisms

Abstract

Let (G, H) be (Ham(R2n), Ham(B2n)) or (B∞, Bn). We conjec- ture 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 c.2018 by the author under Creative Commons Attribution-Noncommercial 3.0 License by using a Bavard-type duality theorem on conjugation invariant norms.