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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 6(384), Pages 91–156 (Mi umn9259)  

This article is cited in 1 scientific paper (total in 1 paper)

Closed 1-forms in topology and dynamics

M. Farber, D. Schütz

University of Durham, UK

Abstract: This article surveys recent progress of results in topology and dynamics based on techniques of closed 1-forms. Our approach lets us draw conclusions about properties of flows by studying homotopical and cohomological features of manifolds. More specifically, a Lusternik–Schnirelmann type theory for closed 1-forms is described, along with the focusing effect for flows and the theory of Lyapunov 1-forms. Also discussed are recent results about cohomological treatment of the invariants $\operatorname{cat}(X,\xi)$ and $\operatorname{cat}^1(X,\xi)$ and their explicit computation in certain examples.

DOI: https://doi.org/10.4213/rm9259

Full text: PDF file (1175 kB)
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English version:
Russian Mathematical Surveys, 2008, 63:6, 1079–1139

Bibliographic databases:

UDC: 515.165
MSC: Primary 37B30, 55M30, 58E05; Secondary 37C29, 57R70
Received: 01.07.2008

Citation: M. Farber, D. Schütz, “Closed 1-forms in topology and dynamics”, Uspekhi Mat. Nauk, 63:6(384) (2008), 91–156; Russian Math. Surveys, 63:6 (2008), 1079–1139

Citation in format AMSBIB
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\by M.~Farber, D.~Sch\"utz
\paper Closed 1-forms in topology and dynamics
\jour Uspekhi Mat. Nauk
\yr 2008
\vol 63
\issue 6(384)
\pages 91--156
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\transl
\jour Russian Math. Surveys
\yr 2008
\vol 63
\issue 6
\pages 1079--1139
\crossref{https://doi.org/10.1070/RM2008v063n06ABEH004579}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65649112432}


Linking options:
  • http://mi.mathnet.ru/eng/umn9259
  • https://doi.org/10.4213/rm9259
  • http://mi.mathnet.ru/eng/umn/v63/i6/p91

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Farber, R. Geoghegan, D. Schütz, “Closed 1-forms in topology and geometric group theory”, Russian Math. Surveys, 65:1 (2010), 143–172  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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