Efficient subdivision in hyperbolic groups and applications
Uri Bader
Weizmann Institute of Science, Rehovot, IsraelAlex Furman
University of Illinois at Chicago, USARoman Sauer
Karlsruher Institut für Technologie, Germany
![Efficient subdivision in hyperbolic groups and applications cover](/_next/image?url=https%3A%2F%2Fcontent.preview.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-7-issue-2.png&w=3840&q=90)
Abstract
We identify the images of the comparison maps from ordinary homology and Sobolev homology, respectively, to the -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 -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 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