[Papers] [Alex Furman]

Efficient subdivision in hyperbolic groups and applications

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 at least 3 and surface groups are rigid with respect to integrable measure equivalence. Moreover, we prove a proportionality principle for the simplicial volume of negatively curved manifolds with regard to integrable measure equivalence.


Authors: U. Bader, A. Furman, R. Sauer
Bibliographical: Groups Geom. Dyn. 7 (2013), no. 2, 263 – 292.
Download: pdfarXiv:1003.1562



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[Papers] [Alex Furman]