Topology of closed 1-forms and their critical points

Michael Farber

doi:10.1016/S0040-9383(99)00059-2

Topology of closed 1-forms and their critical points

Michael Farber^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper we suggest an analog of the Lusternik-Schnirelman theory for closed 1-forms. Namely, we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.

Original language	English
Pages (from-to)	235-258
Number of pages	24
Journal	Topology
Volume	40
Issue number	2
DOIs	https://doi.org/10.1016/S0040-9383(99)00059-2
State	Published - Mar 2001

Keywords

58Exx
Closed 1-forms
Lusternik-Schnirelman theory
Massey products
Morse theory

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10.1016/S0040-9383(99)00059-2

Cite this

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abstract = "In this paper we suggest an analog of the Lusternik-Schnirelman theory for closed 1-forms. Namely, we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.",

keywords = "58Exx, Closed 1-forms, Lusternik-Schnirelman theory, Massey products, Morse theory",

author = "Michael Farber",

note = "Funding Information: The research was supported by a grant from the Israel Academy of Sciences and Humanities and by the Herman Minkowski Center for Geometry. ",

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AB - In this paper we suggest an analog of the Lusternik-Schnirelman theory for closed 1-forms. Namely, we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.

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KW - Closed 1-forms

KW - Lusternik-Schnirelman theory

KW - Massey products

KW - Morse theory

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Topology of closed 1-forms and their critical points

Abstract

Keywords

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