## Geometry Seminar - Abstracts

### Talk

18 May 2016, 16:00 - 17:00, in HG00.310

**Francesca Arici**
(Radboud Universiteit)

*Noncommutative line bundles and Pimsner algebras*

### Abstract

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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