Extending higher-dimensional quasi-cocycles
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Date
2015-12
Publication Type
Journal Article
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yes
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Abstract
Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infinite-dimensional. Our proof is based on an extension to higher degrees of a recent result by Hull and Osin. Namely, we prove that, if H is a hyperbolically embedded subgroup of G and V is any G-module, then any n-quasi cocycle on H with values in V may be extended to G. Also, we show that our extensions detect the geometry of the embedding of hyperbolically embedded subgroups, in a suitable sense.
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published
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Volume
8 (4)
Pages / Article No.
1123 - 1155
Publisher
Wiley
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Organisational unit
09561 - Sisto, Alessandro (ehemalig) / Sisto, Alessandro (former)
08802 - Iozzi, Alessandra (Tit.-Prof.)