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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.
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
Linking options:
https://www.mathnet.ru/eng/rm9259https://doi.org/10.1070/RM2008v063n06ABEH004579 https://www.mathnet.ru/eng/rm/v63/i6/p91
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Abstract page: | 777 | Russian version PDF: | 317 | English version PDF: | 11 | References: | 82 | First page: | 19 |
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