The Fine Structure of the Kasparov Groups II: topologizing the UCT

The Kasparov groups KK_*(A, B) have a natural structure as pseudopolonais groups. In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splittings of the UCT constructed by J. Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses. We show that the various topologies on Ext_{\Bbb Z}^1(K_*(A), K_*(B)) and other related groups mostly coincide. Then we focus attention on the Milnor sequence and the fine structure subgroup of KK_*(A, B). An important consequence of our work is that under bootstrap hypotheses the closure of zero of KK_*(A, B) is isomorphic to the group Pext_{\Bbb Z}^1(K_*(A), K_*(B)). Finally, we introduce new splitting obstructions for the Milnor and Jensen sequences and prove that these sequences split if K_*(A) or K_*(B) is torsion free.Comment: 25 page

The mathematical research of William Parry FRS

In this article we survey the mathematical research of the late William (Bill) Parry, FRS

Transference in spaces of measures

The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many problems in diverse areas, which before were proved by a variety of methods. The purpose of this paper is to bring about a similar approach to the study of measures. Specifically, deep results in classical harmonic analysis and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others, are all extensions of the classical F.&M. Riesz Theorem. We will show that all these extensions are obtainable via our new transference principle for spaces of measures.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints