Geometry Seminar - Abstracts


18 May 2016, 16:00 - 17:00, in HG00.310
Francesca Arici (Radboud Universiteit)
Noncommutative line bundles and Pimsner algebras


In this talk we focus on a noncommutative approach to line bundles. At the C*-algebraic level, line bundles are self-Morita equivalence bimodules E for a C*-algebra B which we think of as the 'base space' algebra. I will describe the C*-algebraic Picard group and its connection to the classical one. The associated bundle construction can also be translated in the noncommutative language by using Pimsner algebras. I will describe this construction providing some examples. Moreover, I will elaborate on naturally arising six term exact sequences in KK-theory, which are the analogue of the Gysin sequence for circle bundles, presenting the computation of K-groups of quantum lens spaces.

Based on joint work with S. Brain, F. D' Andrea, J. Kaad, G. Landi.

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