Quasimorphisms on nonorientable surface diffeomorphism groups
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910686104256512 |
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| author | Kimura, Mitsuaki Kuno, Erika |
| author_facet | Kimura, Mitsuaki Kuno, Erika |
| contents | 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 $\widetilde{QH}(\mathrm{Diff}_0(N_g))$ on the identity component of the diffeomorphism group $\mathrm{Diff}_0(N_g)$ on a closed nonorientable surface $N_g$ of genus $g\geq 3$ is infinite-dimensional. As a corollary, we obtain the unboundedness of the commutator length and the fragmentation length on $\mathrm{Diff}_0(N_g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05540 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasimorphisms on nonorientable surface diffeomorphism groups Kimura, Mitsuaki Kuno, Erika Geometric Topology Group Theory 20F65, 57K20, 57S05 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 $\widetilde{QH}(\mathrm{Diff}_0(N_g))$ on the identity component of the diffeomorphism group $\mathrm{Diff}_0(N_g)$ on a closed nonorientable surface $N_g$ of genus $g\geq 3$ is infinite-dimensional. As a corollary, we obtain the unboundedness of the commutator length and the fragmentation length on $\mathrm{Diff}_0(N_g)$. |
| title | Quasimorphisms on nonorientable surface diffeomorphism groups |
| topic | Geometric Topology Group Theory 20F65, 57K20, 57S05 |
| url | https://arxiv.org/abs/2111.05540 |