Large scale geometry is the study of geometric objects viewed from a great distance. The
idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of …

To every discrete metric space with bounded geometry X we associate a groupoid G (X) for
which the coarse assembly map for X is equivalent to the Baum–Connes assembly map for …

The Baum-Connes Conjecture for Groupoids Page 1 The Baum-Connes Conjecture for
Groupoids Jean-Louis Th Institut de Mathematiques Universite Pierre et Marie Curie 4, place …

The coarse geometric Novikov conjecture provides an algorithm to determine when the
higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this …

In this paper, the first of a series of two, we continue the study of higher index theory for
expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs …

Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a
weak form of amenability and which has important applications to the Novikov conjecture …

Localization Algebras and the Coarse Baum–Connes Conjecture Page 1 K-Theory 11: 307–318,
1997. 307 c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Localization …

We define and study a notion of discrete homology theory for metric spaces. Instead of
working with simplicial homology, our chain complexes are given by Lipschitz maps from an …

We study which von Neumann algebras can be embedded into uniform Roe algebras and
quasi-local algebras associated to a uniformly locally finite metric space X. Under weak …

We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces,
which is a generalization of Gromovʼs notion of coarse embedding into Hilbert space. It …