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15 February 2001 Curvature and characteristic numbers of hyper-Kähler manifolds
Nigel Hitchin, Justin Sawon
Duke Math. J. 106(3): 599-615 (15 February 2001). DOI: 10.1215/S0012-7094-01-10637-6

Abstract

Characteristic numbers of compact hyper-Kähler manifolds are expressed in graph-theoretical form, considering them as a special case of the curvature invariants introduced by L. Rozansky and E. Witten. The appropriate graphs are generated by "wheels," and the recently proved Wheeling theorem is used to give a formula for the $\mathscr{L}$2-norm of the curvature of an irreducible hyper-Kähler manifold in terms of the volume and Pontryagin numbers. The formula involves the multiplicative sequence that is the square root of the Â-polynomial.

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Nigel Hitchin. Justin Sawon. "Curvature and characteristic numbers of hyper-Kähler manifolds." Duke Math. J. 106 (3) 599 - 615, 15 February 2001. https://doi.org/10.1215/S0012-7094-01-10637-6

Information

Published: 15 February 2001
First available in Project Euclid: 13 August 2004

zbMATH: 1024.53032
MathSciNet: MR1813238
Digital Object Identifier: 10.1215/S0012-7094-01-10637-6

Subjects:
Primary: 53C26
Secondary: 32J27, 57M27, 57R20

Rights: Copyright © 2001 Duke University Press

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Vol.106 • No. 3 • 15 February 2001
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