K-theory correspondences and the Fourier-Mukai transform
Date
2019-05-02
Authors
Hudson, Daniel
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Abstract
The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the ideas Connes and Skandalis, and then to apply this machinery to give a geometric proof of a result of Emerson. We begin by giving an overview of topological K-theory, necessary for developing bivariant K-theory. Then we discuss Kasparov's analytic bivariant K-theory, and from there develop topological bivariant K-theory. In the final chapter we state and prove the result of Emerson.
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Keywords
K-Theory, Algebraic Topology, KK-Theory, Operator Algebras, Non-Commutative Geometry