We identify the images of the comparison maps from ordinary homology and Sobolev homology, respectively, to the l1-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 l1-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 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.
1
Weizmann Institute of Science, Rehovot, Israel
2
University of Illinois at Chicago, USA
3
Karlsruher Institut für Technologie, Germany
Uri Bader; Alex Furman; Roman Sauer. Efficient subdivision in hyperbolic groups and applications. Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 263-292. doi: 10.4171/ggd/182
@article{10_4171_ggd_182,
author = {Uri Bader and Alex Furman and Roman Sauer},
title = {Efficient subdivision in hyperbolic groups and applications},
journal = {Groups, geometry, and dynamics},
pages = {263--292},
year = {2013},
volume = {7},
number = {2},
doi = {10.4171/ggd/182},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/182/}
}
TY - JOUR
AU - Uri Bader
AU - Alex Furman
AU - Roman Sauer
TI - Efficient subdivision in hyperbolic groups and applications
JO - Groups, geometry, and dynamics
PY - 2013
SP - 263
EP - 292
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IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/182/
DO - 10.4171/ggd/182
ID - 10_4171_ggd_182
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/182/
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