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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Splitting the curvature
of the determinant line bundle


Author: Simon Scott
Journal: Proc. Amer. Math. Soc. 128 (2000), 2763-2775
MSC (1991): Primary 58G20, 58G26; Secondary 81T50
Published electronically: December 7, 1999
MathSciNet review: 1662210
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold $M=X^{0}\cup X^{1}$ has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves.


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Additional Information

Simon Scott
Affiliation: Department of Mathematics, King’s College, Strand, London WC2R 2LS, United Kingdom
Email: sscott@mth.kcl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05311-3
PII: S 0002-9939(99)05311-3
Keywords: Determinant line bundle, elliptic family, Grassmann section, regularized determinant, splitting principle
Received by editor(s): September 30, 1998
Published electronically: December 7, 1999
Dedicated: Dedicado a la memoria de Hugo Rojas 1973-1997
Communicated by: Peter Li
Article copyright: © Copyright 2000 American Mathematical Society