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

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.

9 pages; surveyish note without original results; v2: corrected arxiv title

References in corpus (1)

• Lipschitz Simplicial Volume of Connected Sums