Ranks of Collinear Morse Forms

Author: Irina Gelbukh

J. Geom. Phys., vol. 61, no. 2, pp. 425-435, 2011.

Abstract: On a smooth closed $n$-manifold, we consider Morse forms with wedge-product zero; we call such forms collinear. This is an equivalence relation. Collinearity classes are classified by the underlying foliation; so, in other words, we study the set of Morse forms that define the same foliation. We describe the set of the ranks of such forms and show how it is related to the structure of the foliation and the manifold.

Keywords: Collinear Morse forms, Morse form foliation, form's rank, minimal components, compact leaves

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