JournalsjncgVol. 10, No. 1pp. 29–64

Pimsner algebras and Gysin sequences from principal circle actions

  • Francesca Arici

    Radboud University Nijmegen, Netherlands
  • Jens Kaad

    Radboud University Nijmegen, Netherlands
  • Giovanni Landi

    Università di Trieste, Italy
Pimsner algebras and Gysin sequences from principal circle actions cover
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Abstract

A self Morita equivalence over an algebra BB, given by a BB-bimodule EE, is thought of as a line bundle over BB. The corresponding Pimsner algebra OE\mathcal O_E is then the total space algebra of a noncommutative principal circle bundle over BB. A natural Gysin-like sequence relates the KKKK-theories of OE\mathcal O_E and of BB. Interesting examples come from OE\mathcal O_E a quantum lens space over BB a quantum weighted projective line (with arbitrary weights). The KKKK-theory of these spaces is explicitly computed and natural generators are exhibited.

Cite this article

Francesca Arici, Jens Kaad, Giovanni Landi, Pimsner algebras and Gysin sequences from principal circle actions. J. Noncommut. Geom. 10 (2016), no. 1, pp. 29–64

DOI 10.4171/JNCG/228