Quasimorphisms on nonorientable surface diffeomorphism groups

2021/11/10 by Kimura, Mitsuaki, Kuno, Erika
#20F65 #57K20 #57S05 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2111.05540

Abstract

Bowden, Hensel, and Webb constructed infinitely many quasimorphisms on the diffeomorphism groups of orientable surfaces. In this paper, we extend their result to nonorientable surfaces. Namely, we prove that the space of nontrivial quasimorphisms \widetildeQH(Diff₀(N_g)) on the identity component of the diffeomorphism group Diff₀(N_g) on a closed nonorientable surface N_g of genus g≥ 3 is infinite-dimensional. As a corollary, we obtain the unboundedness of the commutator length and the fragmentation length on Diff₀(N_g).

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