Closed 1-forms in topology and dynamics

Details Closed 1-forms in topology and dynamics Closed 1-forms in topology and dynamics

2008-07-21

arxiv.org/abs/0807.3240v2

Mathematics

Algebraic Topology

65 pages, 12 figures

Scientific paper

10.1070/RM2008v063n06ABEH004579

This article surveys recent progress of results in topology and dynamics based on techniques of closed one-forms. Our approach allows us to draw conclusions about properties of flows by studying homotopical and cohomological features of manifolds. More specifically we describe a Lusternik - Schnirelmann type theory for closed one-forms, the focusing effect for flows and the theory of Lyapunov one-forms. We also discuss recent results about cohomological treatment of the invariants cat(X, \xi) and cat^1(X, \xi) and their explicit computation in certain examples.

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