Coronae of relatively hyperbolic groups and coarse cohomologies

Tomohiro Fukaya, Shin Ichi Oguni

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)431-474
ページ数44
ジャーナルJournal of Topology and Analysis
8
3
DOI
出版ステータスPublished - 2016 9 1

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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