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arXiv · 1303.1865

Coronae of relatively hyperbolic groups and coarse cohomologies

Tomohiro Fukaya·Shin-ichi Oguni
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Abstract

We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the $K$-homology of the corona with the $K$-theory of the Roe algebra, via the coarse assembly map. We also establish a dual theory, that is, we relate the $K$-theory of the corona with the $K$-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 $K$-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.

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Tomohiro Fukaya, Shin-ichi Oguni. 2014-10-08. Coronae of relatively hyperbolic groups and coarse cohomologies. https://doi.org/10.1142/s1793525316500151

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