Coarse geometry and Callias quantisation

Coarse Geometry and Randomness

1 Introductory graph and metric notions 5 1.1 The Cheeger constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Expander graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Isoperimetric dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Rough isome...

Coarse geometry and asymptotic dimension

We prove that two spaces, whose coarse structures are induced by metrisable compactifications, are coarsely equivalent if and only if their (Higson) coronas are homeomorphic. We introduce translation C∗-algebras for coarse spaces which admit a countable, uniformly bounded cover using projection-valued measures. This was already done in [Roe03]. Here we give a more complete exposition on the sub...

Coarse Geometry and K-homology

Coarse Geometry via Grothendieck Topologies

In the course of the last years several authors have studied index problems for open Riemannian manifolds. The abstract indices are elements in the K-theory of an associated C∗-algebra, which only depends on the ”coarse” (or large scale) geometry of the underlying metric space. In order to make these indices computable J.Roe introduced a new cohomology theory, called coarse cohomology, which is...

Coarse Geometry and P. A. Smith Theory

We define a generalization of the fixed point set, called the bounded fixed set, for a group acting by isometries on a metric space. An analogue of the P. A. Smith theorem is proved for metric spaces of finite asymptotic dimension, which relates the coarse homology of the bounded fixed set to the coarse homology of the total space.