On boundedness of characteristic class via quasi-morphism

Kawasaki, Morimichi; Maruyama, Shuhei

doi:10.48550/arxiv.2012.10612

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2021

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“…This isomorphism was obtained in [KM20] in a different way and applied to study boundedness of characteristic classes of foliated bundles.…”

Section: Proof Of Theoremmentioning

confidence: 99%

The space of non-extendable quasimorphisms

Kawasaki¹,

Kimura²,

Maruyama³

et al. 2021

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In the present paper, 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 commutator subgroup of a Gromov hyperbolic group, the kernel of the (volume) flux homomorphism, and the IA-automorphism group of a free group. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the mixed stable commutator length for certain pairs of a group and its normal subgroup.

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“…This isomorphism was obtained in [KM20] in a different way and applied to study boundedness of characteristic classes of foliated bundles.…”

Section: Proof Of Theoremmentioning

confidence: 99%