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Holomorphic one-forms, fibrations over the circle, and characteristic numbers of Kähler manifolds

Part of: Differential topology Complex manifolds Homology and cohomology theories

Published online by Cambridge University Press:  26 February 2021

D. KOTSCHICK
D. KOTSCHICK*
Affiliation:
Mathematisches Institut, LMU München, Theresienstr. 39, 80333München, Germany. e-mail: [email protected]
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Abstract

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We prove that the only relation imposed on the Hodge and Chern numbers of a compact Kähler manifold by the existence of a nowhere zero holomorphic one-form is the vanishing of the Hirzebruch genus. We also treat the analogous problem for nowhere zero closed one-forms on smooth manifolds.

MSC classification

Primary: 32Q15: Kähler manifolds
Secondary: 32Q55: Topological aspects of complex manifolds 55N22: Bordism and cobordism theories, formal group laws 57R20: Characteristic classes and numbers
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 95 - 103
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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