The coarse shape groups

Shape-Based Coarse Graining

Coarse Median Spaces and Groups

We introduce the notion of a coarse median on a metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of such a median on a geodesic space is quasi-isometry invariant, and so applies to finitely generated groups via their Cayley graphs. We show that asymptotic cones of such spaces are topological median algebras. We define a notion of rank for a coars...

Groups with no coarse embeddings into hyperbolic groups

We introduce an obstruction to the existence of a coarse embedding of a given group or space into a hyperbolic group, or more generally into a hyperbolic graph of bounded degree. The condition we consider is “admitting exponentially many fat bigons”, and it is preserved by a coarse embedding between graphs with bounded degree. Groups with exponential growth and linear divergence (such as direct...

Coarse view synthesis using shape-from-shading

This paper investigates the use of shape-from-shading for coarse view synthesis. The aim of our study is to determine whether needle-maps delivered by a new shape-from-shading (SFS) algorithm can be used as a compact object-representation for the purposes of e3ciently generating appearance manifolds. Speci4cally, we aim to show that the needle-maps can be used to generate novel object views und...

Coarse Alexander Duality and Duality Groups

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n − 1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action G y X determines a collection of “peripheral” subgroups H1, . . . , Hk ⊂ G so that the...