A real-valued function "close to a homomorphism" on a group is called a quasimorphism. Quasimorphisms have appeared in many contexts, including geometric group theory and topology, and have been of interest, but their construction is difficult in general. Recently, Bowden, Hensel, and Webb proved that there exists infinitely many quasimorphisms on surface diffeomorphism groups. This is in contrast to the case of higher dimensional manifolds. Their method is an analogy of the construction in the case of mapping class groups by Bestvina and Fujiwara. This is interesting in that the techniques used for discrete groups are applied to diffeomorphism groups. In this talk, I will explain their method and its generalization to nonorientable surfaces by Erika Kuno (Osaka) and the speaker.

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