|XXXVIII Workshop on Geometric Methods in Physics||30.06-6.07.2019|
|VIII School on Geometry and Physics||24-28.06.2019|
Circle and sphere bundles in noncommutative geometry
In this talk I will recall how Pimsner algebras of self Morita equivalences can be thought of as total spaces of quantum circle bundles, and the associated six term exact sequence in K-theory can be interpreted as an operator algebraic version of the classical Gysin sequence for circle bundles. After reviewing some results in this direction, I will report on work in progress concerning the construction of higher dimensional quantum sphere bundles in terms of Cuntz-Pimsner algebras of sub-product systems. Based on (ongoing) joint work with G. Landi and J. Kaad.
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