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arXiv · 1401.6788

The Gysin Sequence for Quantum Lens Spaces

Francesca Arici·Simon Brain·Giovanni Landi
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Abstract

We define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.

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BibTeXRIS

Francesca Arici, Simon Brain, Giovanni Landi. 2014-01-27. The Gysin Sequence for Quantum Lens Spaces. https://doi.org/10.4171/jncg/216

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