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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 splitting sof 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 [cursive]Ext^{1}_{ℤ}(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 [cursive]Pext^{1}_{ℤ}(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 torsionfree.


Analysis | Geometry and Topology


This is the author’s final accepted manuscript version of a work, derived from arXiv [], and subsequently accepted for publication in the Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 194(2) (2002) []

1991 Mathematics Subject Classification: Primary 19K35, 46L80, 47A66; Secondary 19K56, 47C15.