448 research outputs found
On coarse embeddability into -spaces and a conjecture of Dranishnikov
We show that the Hilbert space is coarsely embeddable into any for
. In particular, this yields new characterizations of
embeddability of separable metric spaces into the Hilbert space.Comment: 5 page
Aperiodic tilings of manifolds of intermediate growth
We give a homological construction of aperiodic tiles for certain open
Riemannian surfaces admitting actions of Grigorchuk groups of intermediate
growth.Comment: Accepted for publication in Groups, Geometry and Dynamic
Eilenberg swindles and higher large scale homology of products of trees
We show that uniformly finite homology of products of trees vanishes in
all degrees except degree , where it is infinite dimensional. Our method is
geometric and applies to several large scale homology theories, including
almost equivariant homology and controlled coarse homology. As an application
we determine group homology with -coefficients of lattices in
products of trees. We also show a characterization of amenability in terms of
1-homology and construct aperiodic tilings using higher homology.Comment: Final version, to appear in Groups, Geometry & Dynamic
Hilbert C*-modules and amenable actions
We study actions of discrete groups on Hilbert -modules induced from
topological actions on compact Hausdorff spaces. We show non-amenability of
actions of non-amenable and non-a-T-menable groups, provided there exists a
quasi-invariant probability measure which is sufficiently close to being
invariant.Comment: Final version, to appear in Studia Mathematic
Expanders are counterexamples to the coarse -Baum-Connes conjecture
We show that certain expanders are counterexamples to the coarse
-Baum-Connes conjecture.Comment: 19 page
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