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arXiv · 2005.02187

Honours thesis: Exact sequences in graded $KK$-theory for Cuntz-Pimsner algebras

Quinn Patterson
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Abstract

In this thesis we generalise the six-term exact sequence in graded $KK$-theory obtained in a paper of Kumjian, Pask and Sims (2017) to allow correspondences with non-compact left action. In particular, this allows us to compute the graded $KK$-theory of row-infinite graphs. We develop the theory necessary for following the arguments of Kumjian, Pask and Sims and of Pimsner (1997), with detailed sections on Hilbert modules, $C^*$-correspondences, Crossed products, Toeplitz algebras, Cuntz-Pimsner algebras and $KK$-theory.

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Quinn Patterson. 2020-05-02. Honours thesis: Exact sequences in graded $KK$-theory for Cuntz-Pimsner algebras. https://arxiv.org/abs/2005.02187

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