26 citations · 42 across the 13 of their papers we have counts for
13 papers
E-theory for -Categories
Sarah L. Browne, Paul D. Mitchener
-theory was originally defined concretely by Connes and Higson and further work followed this construction. We generalise the definition to -categories. -categor…
Coarse Homotopy Groups
Paul D. Mitchener, Behnam Norouzizadeh, Thomas Schick
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse…
Descent and the -assembly map
Paul D. Mitchener
In this article we show that a general notion of descent in coarse geometry can be applied to the study of injectivity of the -assembly map. We also show that the coarse assemb…
An Analytic Novikov Conjecture for Semigroups
Paul D. Mitchener
In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises eff…
The General Notion of Descent in Coarse Geometry
Paul D. Mitchener
In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. F…
The -theory spectrum of the reduced group -algebra is a functor
Paul D. Mitchener
We construct -categories that are anologues of the categories used in controlled algebraic -theory. We then show that the reduced -algebra of a finitely presente…