Morse theory of harmonic forms
dg-ga
2007-05-23 v1 Differential Geometry
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.
Cite
@article{arxiv.dg-ga/9711007,
title = {Morse theory of harmonic forms},
author = {Michael Farber and Gabriel Katz and Jerome Levine},
journal= {arXiv preprint arXiv:dg-ga/9711007},
year = {2007}
}
Comments
16 pages, AMSTex, 12 figures