Work

Quasimorphisms on nonorientable surface diffeomorphism groups

Year: 2025

Type: article

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 Q H ˜ Diff 0 N g $\widetilde{Q H}\left(\operatorname{Diff}_0\left(N_g\right)\right)$ on the identity component of the diffeomorphism group Diff0(Ng ) on a closed nonorientable surface Ng of genus g ≥ 3 is infinite-dimensional. As a corollary, we obtain the unboundedness of the commutator length and the fragmentation length on Diff0(Ng ).

Source: Advances in Geometry

DOI: 10.1515/advgeom-2025-0011

Authors: Mitsuaki Kimura, Erika Kuno

Institutions: Osaka Dental University, The University of Osaka

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, JST-Mirai Program, ACT-X

Awards: G2096268528, G6764570186, Studies on quasi-isometry classification of mapping class groups and their subgroups using distortion