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Line bundles and the Thom construction in noncommutative geometry

Edwin Beggs Orcid Logo, Tomasz Brzeziński, Tomasz Brzezinski Orcid Logo

Journal of Noncommutative Geometry, Volume: 8, Issue: 1, Pages: 61 - 105

Swansea University Authors: Edwin Beggs Orcid Logo, Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.4171/JNCG/149

Abstract

The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we c...

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Published in: Journal of Noncommutative Geometry
ISSN: 1661-6952 1661-6960
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa13888
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spelling 2015-07-31T16:33:52.6322321 v2 13888 2013-01-15 Line bundles and the Thom construction in noncommutative geometry a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2013-01-15 SMA The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we construct a positive integer graded module. This corresponds to the topological Thom construction and associated circle bundle for a line bundle. In the case that the original algebra is a C* algebra, with some positivity assumptions, the Thom construction gives another C* algebra.The paper ends by a study of the de Rham characteristic classes of a NC line module using the methods of Kobayashi and Nomizu. Journal Article Journal of Noncommutative Geometry 8 1 61 105 1661-6952 1661-6960 Noncommutative geometry, line bundle, Chern class, Thom construction 31 12 2014 2014-12-31 10.4171/JNCG/149 http://www.ems-ph.org/journals/journal.php?jrn=JNCG Accepted for publication May 2012. COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-07-31T16:33:52.6322321 2013-01-15T09:36:46.5773307 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Edwin Beggs 0000-0002-3139-0983 1 Tomasz Brzeziński 2 Tomasz Brzezinski 0000-0001-6270-3439 3
title Line bundles and the Thom construction in noncommutative geometry
spellingShingle Line bundles and the Thom construction in noncommutative geometry
Edwin Beggs
Tomasz Brzezinski
title_short Line bundles and the Thom construction in noncommutative geometry
title_full Line bundles and the Thom construction in noncommutative geometry
title_fullStr Line bundles and the Thom construction in noncommutative geometry
title_full_unstemmed Line bundles and the Thom construction in noncommutative geometry
title_sort Line bundles and the Thom construction in noncommutative geometry
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Edwin Beggs
Tomasz Brzezinski
author2 Edwin Beggs
Tomasz Brzeziński
Tomasz Brzezinski
format Journal article
container_title Journal of Noncommutative Geometry
container_volume 8
container_issue 1
container_start_page 61
publishDate 2014
institution Swansea University
issn 1661-6952
1661-6960
doi_str_mv 10.4171/JNCG/149
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://www.ems-ph.org/journals/journal.php?jrn=JNCG
document_store_str 0
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description The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we construct a positive integer graded module. This corresponds to the topological Thom construction and associated circle bundle for a line bundle. In the case that the original algebra is a C* algebra, with some positivity assumptions, the Thom construction gives another C* algebra.The paper ends by a study of the de Rham characteristic classes of a NC line module using the methods of Kobayashi and Nomizu.
published_date 2014-12-31T03:15:52Z
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