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The space of
nonextendable quasimorphisms
Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama, Takahiro Matsushita and Masato Mimura |
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Algebraic & Geometric Topology 25 (2025) 1169–1226
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Abstract |
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For a pair of a group with normal subgroup , we consider the space of quasimorphisms and quasicocycles on nonextendable to . To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As an 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 normal subgroup. |
Keywords
bounded cohomology, invariant quasimorphisms, group
cohomology, bounded acyclicity
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Mathematical Subject Classification
Primary: 20J06
Secondary: 20F65, 20J05, 57M07
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References |
Publication
Received: 16 August 2023
Revised: 1 February 2024
Accepted: 25 February 2024
Published: 16 May 2025
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Authors |
| Morimichi Kawasaki | |
| Department of Mathematics Faculty of Science Hokkaido University Sapporo Japan |
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| Mitsuaki Kimura | |
| Department of Mathematics Osaka Dental University Hirakata Japan |
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| Shuhei Maruyama | |
| School of Mathematics and
Physics College of Science and Engineering Kanazawa University Kanazawa Japan |
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| Takahiro Matsushita | |
| Department of Mathematical
Sciences Faculty of Science Shinshu University Matsumoto Japan |
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| Masato Mimura | |
| Mathematical Institute Tohoku University Sendai Japan |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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