A self Morita equivalence over an algebra , given by a -bimodule , is thought of as a line bundle over . The corresponding Pimsner algebra is then the total space algebra of a noncommutative principal circle bundle over . A natural Gysin-like sequence relates the -theories of and of . Interesting examples come from a quantum lens space over a quantum weighted projective line (with arbitrary weights). The -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. 29–64DOI 10.4171/JNCG/228