Abstract
A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O E is then the total space algebra of a non-commutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O E and of B. Interesting examples come from O E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.
Original language | English |
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Journal | Journal of Noncommutative Geometry |
Volume | 10 |
Issue number | 1 |
Pages (from-to) | 29-64 |
ISSN | 1661-6952 |
DOIs | |
Publication status | Published - 2016 |
Externally published | Yes |
Keywords
- Circle actions
- Gysin sequences
- KK-theory
- Pimsner algebras
- Quantum lens spaces
- Quantum principal bundles
- Quantum weighted projective spaces