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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Functorial Hodge identities and quantization


Author: M. J. Slupinski
Journal: Trans. Amer. Math. Soc. 355 (2003), 2011-2046
MSC (2000): Primary 22E99, 53C50, 53C55, 53C99
Published electronically: January 10, 2003
MathSciNet review: 1953536
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Abstract: By a uniform abstract procedure, we obtain integrated forms of the classical Hodge identities for Riemannian, Kähler and hyper-Kähler manifolds, as well as of the analogous identities for metrics of arbitrary signature. These identities depend only on the type of geometry and, for each of the three types of geometry, define a multiplicative functor from the corresponding category of real, graded, flat vector bundles to the category of infinite-dimensional $\mathbf{Z}_{2}$-projective representations of an algebraic structure. We define new multiplicative numerical invariants of closed Kähler and hyper-Kähler manifolds which are invariant under deformations of the metric.


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Additional Information

M. J. Slupinski
Affiliation: Université de Louis Pasteur et CNRS (URA 01), 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: slupins@math.u-strasbg.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03208-2
PII: S 0002-9947(03)03208-2
Received by editor(s): April 17, 2002
Received by editor(s) in revised form: July 2, 2002
Published electronically: January 10, 2003
Article copyright: © Copyright 2003 American Mathematical Society