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Line bundles and the Thom construction in noncommutative geometry | | E.J. Beggs
; T. Brzezinski
; | | Date: |
7 Dec 2010 | | Abstract: | The idea of a line bundle in classical geometry is transferred to
noncommutative geometry by the idea of a Morita context. From this we can
construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois
extension. A non-degenerate Hermitian metric gives a star structure on this
algebra, and an additional star operation on the line bundle gives a star
operation on the N graded algebra. In this case, we can carry out the
associated circle bundle and Thom constructions. Starting with a C* algebra as
base, and with some positivity assumptions, the associated circle and Thom
algebras are also C* algebras. We conclude by examining covariant derivatives
on line bundles. | | Source: | arXiv, 1012.1475 | | Services: | Forum | Review | PDF | Favorites | |
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