JournalsggdVol. 7, No. 2pp. 263–292

Efficient subdivision in hyperbolic groups and applications

  • Uri Bader

    Weizmann Institute of Science, Rehovot, Israel
  • Alex Furman

    University of Illinois at Chicago, USA
  • Roman Sauer

    Karlsruher Institut für Technologie, Germany
Efficient subdivision in hyperbolic groups and applications cover
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Abstract

We identify the images of the comparison maps from ordinary homology and Sobolev homology, respectively, to the 1\ell^1-homology of a word-hyperbolic group with coefficients in complete normed modules. The underlying idea is that there is a subdivision procedure for singular chains in negatively curved spaces that is much more efficient (in terms of the 1\ell^1-norm) than barycentric subdivision. The results of this paper are an important ingredient in a forthcoming proof of the authors that hyperbolic lattices in dimension 3\ge 3 are rigid with respect to integrable measure equivalence. Moreover, we prove a new proportionality principle for the simplicial volume of manifolds with word-hyperbolic fundamental groups.

Cite this article

Uri Bader, Alex Furman, Roman Sauer, Efficient subdivision in hyperbolic groups and applications. Groups Geom. Dyn. 7 (2013), no. 2, pp. 263–292

DOI 10.4171/GGD/182