We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

%B Noncommutative Analysis, Operator Theory and Applications %I Springer International Publishing %C Cham %P 1–25 %@ 978-3-319-29116-1 %G eng %U https://doi.org/10.1007/978-3-319-29116-1_1 %R 10.1007/978-3-319-29116-1_1 %0 Journal Article %J Journal of Noncommutative Geometry %D 2016 %T Pimsner algebras and Gysin sequences from principal circle actions %A Francesca Arici %A Jens Kaad %A Giovanni Landi %B Journal of Noncommutative Geometry %V 10 %P 29–64 %G eng %U http://hdl.handle.net/2066/162951 %R 10.4171/jncg/228 %0 Thesis %D 2015 %T Principal circle bundles, Pimsner algebras and Gysin sequences %A Francesca Arici %X Principal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the `base space’ algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces. %I SISSA %G en %1 34744 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Francesca Arici (farici@sissa.it) on 2015-09-26T07:48:48Z No. of bitstreams: 1 AriciThesis.pdf: 983966 bytes, checksum: 4eadf33259d623493f52eaba5c45ec90 (MD5)