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Line bundles over noncommutative spaces

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OASW03 - Subfactors, K-theory and conformal field theory

We give a Pimsner algebra construction of noncommutative lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over noncommutative weighted projective spaces. For each quantum lens space one gets an analogue of the classical Gysin sequence relating the KK theory of the total space algebra to that of the base space one. This can be used to give explicit geometric representatives of the K-theory classes of the lens spaces. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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