Explicit $\ell^1$-efficient cycles and amenable normal subgroups

Clara Loeh

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arXiv · 1704.05345

Explicit $\ell^1$-efficient cycles and amenable normal subgroups

Clara Loeh

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Abstract

By Gromov's mapping theorem for bounded cohomology, the projection of a group to the quotient by an amenable normal subgroup is isometric on group homology with respect to the $\ell^1$-semi-norm. Gromov's description of the diffusion of cycles also implicitly produces efficient cycles in this situation. We present an elementary version of this explicit construction.

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Clara Loeh. 2017-04-18. Explicit $\ell^1$-efficient cycles and amenable normal subgroups. https://arxiv.org/abs/1704.05345

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