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ON COLLINEAR CLOSED ONE-FORMS

Part of: Differential topology

Published online by Cambridge University Press:  16 June 2011

IRINA GELBUKH
IRINA GELBUKH*
Affiliation:
Waseda Step 21, Room 403, Totsuka-Machi 1-103, Shinjuku-ku, Tokyo 169-0071, Japan (email: gelbukh@member.ams.org)
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Abstract

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We study one-forms with zero wedge-product, which we call collinear, and their foliations. We characterise the set of forms that define a given foliation, with special attention to closed forms and forms with small singular sets. We apply the notion of collinearity to give a criterion for the existence of a compact leaf and to study homological properties of compact leaves.

Keywords

differential one-formsingular setfoliationcompact leavescup-product

MSC classification

Secondary: 57R30: Foliations; geometric theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 322 - 336
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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