Coronae of relatively hyperbolic groups and coarse cohomologies
K-Theory and Homology
2017-05-17 v2
Abstract
We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the -homology of the corona with the -theory of the Roe algebra, via the coarse assembly map. We also establish a dual theory, that is, we relate the -theory of the corona with the -theory of the reduced stable Higson corona via the coarse co-assembly map. For that purpose, we formulate generalized coarse cohomology theories. As an application, we give an explicit computation of the -theory of the Roe-algebra and that of the reduced stable Higson corona of the fundamental groups of closed 3-dimensional manifolds and of pinched negatively curved complete Riemannian manifolds with finite volume.
Keywords
Cite
@article{arxiv.1303.1865,
title = {Coronae of relatively hyperbolic groups and coarse cohomologies},
author = {Tomohiro Fukaya and Shin-ichi Oguni},
journal= {arXiv preprint arXiv:1303.1865},
year = {2017}
}
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48 pages