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15 April 2001 On products of harmonic forms
D. Kotschick
Duke Math. J. 107(3): 521-531 (15 April 2001). DOI: 10.1215/S0012-7094-01-10734-5

Abstract

We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle and are related to symplectic geometry and Seiberg-Witten theory.

We also prove that a manifold admits a metric with harmonic forms whose product is not harmonic if and only if it is not a rational homology sphere.

Citation

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D. Kotschick. "On products of harmonic forms." Duke Math. J. 107 (3) 521 - 531, 15 April 2001. https://doi.org/10.1215/S0012-7094-01-10734-5

Information

Published: 15 April 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1036.53030
MathSciNet: MR1828300
Digital Object Identifier: 10.1215/S0012-7094-01-10734-5

Subjects:
Primary: 53C25
Secondary: 53D35, 57R17, 57R57, 58A14

Rights: Copyright © 2001 Duke University Press

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Vol.107 • No. 3 • 15 April 2001
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