Closed 1-forms in topology and dynamics
Algebraic Topology
2009-11-13 v2 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0807.3240,
title = {Closed 1-forms in topology and dynamics},
author = {Michael Farber and Dirk Schuetz},
journal= {arXiv preprint arXiv:0807.3240},
year = {2009}
}
Comments
65 pages, 12 figures