The Gysin Sequence for Quantum Lens Spaces
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.
Keywords
Cite
@article{arxiv.1401.6788,
title = {The Gysin Sequence for Quantum Lens Spaces},
author = {Francesca Arici and Simon Brain and Giovanni Landi},
journal= {arXiv preprint arXiv:1401.6788},
year = {2016}
}
Comments
27 pages. v2: No changes in the scientific content and results. Section 5 completely re-written and a final section added; suppressed two appendices; added references; minor changes throughout the paper. To appear in the JNcG