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Morse theory of harmonic forms

Michael Farber·Gabriel Katz·Jerome Levine
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Abstract

We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some Riemannian metric. We show that, under suitable assumptions, it is impossible. We use, in an essential way, a theorem of E.Calabi characterizing 1-forms which are harmonic with respect to some metric. We also study some interesting examples illustrating our results.

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BibTeXRIS

Michael Farber, Gabriel Katz, Jerome Levine. 1997-11-11. Morse theory of harmonic forms. https://arxiv.org/abs/dg-ga/9711007

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