700 research outputs found
Geometric Property (T)
This paper discusses `geometric property (T)'. This is a property of metric
spaces introduced in earlier work of the authors for its applications to
K-theory. Geometric property (T) is a strong form of `expansion property': in
particular for a sequence of finite graphs , it is strictly stronger
than being an expander in the sense that the Cheeger constants
are bounded below.
We show here that geometric property (T) is a coarse invariant, i.e. depends
only on the large-scale geometry of a metric space . We also discuss the
relationships between geometric property (T) and amenability, property (T), and
various coarse geometric notions of a-T-menability. In particular, we show that
property (T) for a residually finite group is characterised by geometric
property (T) for its finite quotients.Comment: Version two corrects some typos and a mistake in the proof of Lemma
8.
The Baum-Connes conjecture for hyperbolic groups
We prove the Baum-Connes conjecture for hyperbolic groups and their
subgroups
The coarse geometric Novikov conjecture and uniform convexity
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 paper is to prove the coarse geometric Novikov conjecture
for spaces which admit a (coarse) uniform embedding into a uniformly convex
Banach space.Comment: 64 pages, to appear in Advances in Mathematic
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