Coronae of relatively hyperbolic groups and coarse cohomologies

Tomohiro Fukaya, Shin Ichi Oguni

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)431-474
Number of pages44
JournalJournal of Topology and Analysis
Volume8
Issue number3
DOIs
Publication statusPublished - 2016 Sep 1

Keywords

  • Coarse cohomology
  • coarse assembly map
  • coarse co-assembly map
  • corona
  • relatively hyperbolic group

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Coronae of relatively hyperbolic groups and coarse cohomologies'. Together they form a unique fingerprint.

Cite this