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arXiv · 2107.08571

The space of non-extendable quasimorphisms

Morimichi Kawasaki·Mitsuaki Kimura·Shuhei Maruyama·Takahiro Matsushita·Masato Mimura
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Abstract

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.

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Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama, Takahiro Matsushita, Masato Mimura. 2023-08-16. The space of non-extendable quasimorphisms. https://doi.org/10.2140/agt.2025.25.1169

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