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Weighted Circle Actions on the Heegaard Quantum Sphere

Tomasz Brzeziński, Simon A. Fairfax, Tomasz Brzezinski Orcid Logo

Letters in Mathematical Physics, Volume: 104, Issue: 2, Pages: 195 - 215

Swansea University Author: Tomasz Brzezinski Orcid Logo

DOI (Published version): 10.1007/s11005-013-0664-z

Abstract

Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and their repre- sentations are classified and described on algebraic and topological levels. On the alge- braic side, coordinate algebras of quantum weighted...

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Published in: Letters in Mathematical Physics
Published: 2014
Online Access: http://arxiv.org/abs/1305.5942
URI: https://cronfa.swan.ac.uk/Record/cronfa20518
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spelling 2015-03-27T09:49:50.8931177 v2 20518 2015-03-25 Weighted Circle Actions on the Heegaard Quantum Sphere 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2015-03-25 SMA Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and their repre- sentations are classified and described on algebraic and topological levels. On the alge- braic side, coordinate algebras of quantum weighted Heegaard spheres are interpreted as generalised Weyl algebras, quantum principal circle bundles and Fredholm modules over them are constructed, and the associated line bundles are shown to be non-trivial by an explicit calculation of their Chern numbers. On the topological side, the C∗-algebras of continuous functions on quantum weighted Heegaard spheres are described and their K-groups are calculated. Note: The final publication is available at link.springer.com. Journal Article Letters in Mathematical Physics 104 2 195 215 31 12 2014 2014-12-31 10.1007/s11005-013-0664-z http://arxiv.org/abs/1305.5942 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-03-27T09:49:50.8931177 2015-03-25T09:44:28.6216437 College of Science Mathematics Tomasz Brzeziński 1 Simon A. Fairfax 2 Tomasz Brzezinski 0000-0001-6270-3439 3 0020518-27032015091632.pdf q-heegaard_rev.pdf 2015-03-27T09:16:32.0930000 Output 265170 application/pdf Accepted Manuscript true 2015-03-27T00:00:00.0000000 false
title Weighted Circle Actions on the Heegaard Quantum Sphere
spellingShingle Weighted Circle Actions on the Heegaard Quantum Sphere
Tomasz Brzezinski
title_short Weighted Circle Actions on the Heegaard Quantum Sphere
title_full Weighted Circle Actions on the Heegaard Quantum Sphere
title_fullStr Weighted Circle Actions on the Heegaard Quantum Sphere
title_full_unstemmed Weighted Circle Actions on the Heegaard Quantum Sphere
title_sort Weighted Circle Actions on the Heegaard Quantum Sphere
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzeziński
Simon A. Fairfax
Tomasz Brzezinski
format Journal article
container_title Letters in Mathematical Physics
container_volume 104
container_issue 2
container_start_page 195
publishDate 2014
institution Swansea University
doi_str_mv 10.1007/s11005-013-0664-z
college_str College of Science
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hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
url http://arxiv.org/abs/1305.5942
document_store_str 1
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description Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and their repre- sentations are classified and described on algebraic and topological levels. On the alge- braic side, coordinate algebras of quantum weighted Heegaard spheres are interpreted as generalised Weyl algebras, quantum principal circle bundles and Fredholm modules over them are constructed, and the associated line bundles are shown to be non-trivial by an explicit calculation of their Chern numbers. On the topological side, the C∗-algebras of continuous functions on quantum weighted Heegaard spheres are described and their K-groups are calculated. Note: The final publication is available at link.springer.com.
published_date 2014-12-31T03:30:51Z
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