Duke Mathematical Journal

On products of harmonic forms

D. Kotschick

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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.

Article information

Source
Duke Math. J. Volume 107, Number 3 (2001), 521-531.

Dates
First available in Project Euclid: 5 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1091737022

Digital Object Identifier
doi:10.1215/S0012-7094-01-10734-5

Mathematical Reviews number (MathSciNet)
MR1828300

Zentralblatt MATH identifier
1036.53030

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57R17: Symplectic and contact topology 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]

Citation

Kotschick, D. On products of harmonic forms. Duke Math. J. 107 (2001), no. 3, 521--531. doi:10.1215/S0012-7094-01-10734-5. http://projecteuclid.org/euclid.dmj/1091737022.


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