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2 results

6 - Localisation Algebras and K-homology
from Part Two - Roe Algebras, Localisation Algebras and Assembly
Rufus Willett, University of Hawaii, Manoa, Guoliang Yu, Texas A & M University
Book:

Higher Index Theory

Published online:

11 June 2020

Print publication:

02 July 2020, pp 217-273
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Summary

Introduction to assembly as a 'forget control' map from K-homology to K-theory of Roe algebras.Introduction of the Baum-Connes and coarse Baum-Connes conjectures as universal assembly maps.Concrete models for the Baum-Connes conjecture for special cases, and proof of the coarse Baum-Connes conjecture for Euclidean space.

Classifying Spaces and Boundaries for Relatively Hyperbolic Groups
François Dahmani
Journal:

Proceedings of the London Mathematical Society / Volume 86 / Issue 3 / May 2003

Published online by Cambridge University Press:

09 June 2003, pp. 666-684

Print publication:

May 2003
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We prove the following: if a group $\Gamma$ is torsion-free, and relatively hyperbolic (with the Bounded Coset Penetration property), relative to a subgroup admitting a finite classifying space, then $\Gamma$ admits a finite classifying space. In this case, if the subgroup admits a boundary in the sense of $\mathcal{Z}$-structures, we prove that $\Gamma$ admits a boundary. This extends classical results of Rips, and of Bestvina and Mess to the relative case.

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2 results

6 - Localisation Algebras and K-homology

Summary

Classifying Spaces and Boundaries for Relatively Hyperbolic Groups