The space of non-extendable quasimorphisms
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866918025945415680 |
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| author | Kawasaki, Morimichi Kimura, Mitsuaki Maruyama, Shuhei Matsushita, Takahiro Mimura, Masato |
| author_facet | Kawasaki, Morimichi Kimura, Mitsuaki Maruyama, Shuhei Matsushita, Takahiro Mimura, Masato |
| contents | For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups.
Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08571 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The space of non-extendable quasimorphisms Kawasaki, Morimichi Kimura, Mitsuaki Maruyama, Shuhei Matsushita, Takahiro Mimura, Masato Group Theory Functional Analysis Geometric Topology Symplectic Geometry 20J06, 20J05, 20F65, 57M07 For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup. |
| title | The space of non-extendable quasimorphisms |
| topic | Group Theory Functional Analysis Geometric Topology Symplectic Geometry 20J06, 20J05, 20F65, 57M07 |
| url | https://arxiv.org/abs/2107.08571 |