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Universal Coefficient Theorems and Assembly Maps in KK-Theory

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Topics in Algebraic and Topological K-Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2008))

Abstract

We introduce equivariant Kasparov theory using its universal property and construct the Baum–Connes assembly map by localising the Kasparov category at a suitable subcategory. Then we explain a general machinery to construct derived functors and spectral sequences in triangulated categories. This produces various generalisations of the Rosenberg–Schochet Universal Coefficient Theorem.

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  1. Mathematisches Institut and Courant Centre “Higher Order Structures”, Georg-August-Universität Göttingen, Bunsenstraße 3–5, 37073, Göttingen, Germany

    Ralf Meyer

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Meyer, R. (2011). Universal Coefficient Theorems and Assembly Maps in KK-Theory. In: Topics in Algebraic and Topological K-Theory. Lecture Notes in Mathematics(), vol 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15708-0_2

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