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.