KK-theory of C*-categories and the analytic assembly map

We define KK-theory spectra associated to C*-categories and look at certain instances of the Kasparov product at this level. This machinery is used to give a description of the analytic assembly map as a natural map of spectra.Comment: This is an updated version of an existing article. In this new version the machinery developed works in greater generality than the old versio

The KHKH-Isomorphism Conjecture and Algebraic KKKK-theory

In this article we prove that the $KH$-asembly map, as defined by Bartels and L{\"u}ck, can be described in terms of the algebraic $KK$-theory of Cortinas and Thom. The $KK$-theory description of the $KH$-assembly map is similar to that of the Baum-Connes assembly map. In very elementary cases, methods used to prove the Baum-Connes conjecture also apply to the $KH$-isomorphism conjecture

Coarse homology theories

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the coarse Baum-Connes conjecture for such spaces.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-13.abs.htm

An Analytic Novikov Conjecture for Semigroups

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 effectively to this new situation.Comment: 16 page

Structure-Activity Studies Of 7-Heteroaryl-3-Azabicyclo[3.3.1]Non-6-Enes: A Novel Class Of Highly Potent Nicotinic Receptor Ligands

The potential for nicotinic ligands with affinity for the α4β2 or α7 subtypes to treat such diverse diseases as nicotine addiction, neuropathic pain, and neurodegenerative and cognitive disorders has been exhibited clinically for several compounds while preclinical activity in relevant in vivo models has been demonstrated for many more. For several therapeutic programs, we sought nicotinic ligands with various combinations of affinity and function across both subtypes, with an emphasis on dual α4β2-α7 ligands, to explore the possibility of synergistic effects. We report here the structure-activity relationships (SAR) for a novel series of 7-heteroaryl-3-azabicyclo[3.3.1]non-6-enes and characterize many of the analogues for activity at multiple nicotinic subtypes. © 2012 American Chemical Society