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Gysin Exact Sequences for Quantum Weighted Lens Spaces

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2016 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 1))

Abstract

We describe quantum weighted lens spaces as total spaces of quantum principal circle bundles, using a Cuntz-Pimsner model. The corresponding Pimsner exact sequence is interpreted as a noncommutative analogue of the Gysin exact sequence. We use the sequence to compute the K-theory and K-homology groups of quantum weighted lens spaces, extending previous results and computations due to the author and collaborators.

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Acknowledgements

We thank the mathematical research institute MATRIX in Australia and the organisers of the workshop “Refining C∗-algebraic invariants using KK-theory”, where part of this research was performed. This work was motivated by discussions with Efren Ruiz about the structure of graph algebras. We thank Adam Rennie for helpful discussion and for his hospitality at the University of Wollongong, where part of this work was carried out. Finally, the author would like to thank Francesco D’Andrea, Giovanni Landi, Bram Mesland and Walter van Suijlekom for helpful comments on an early version of this work. This research was partially supported by NWO under the VIDI-grant 016.133.326.

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Authors and Affiliations

  1. Faculty of Science, Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, 6525AJ, Nijmegen, The Netherlands

    Francesca Arici

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  1. Francesca Arici
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Correspondence to Francesca Arici .

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Editors and Affiliations

  1. University of Melbourne, Melbourne, Australia

    Jan de Gier

  2. University of Western Australia, Crawley, Australia

    Cheryl E. Praeger

  3. UCLA, Los Angeles, USA

    Terence Tao

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Arici, F. (2018). Gysin Exact Sequences for Quantum Weighted Lens Spaces. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_12

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