Group actions on bifoliated planes and classification of (pseudo)-Anosov flows in dimension 3

Abstract: An old problem in dynamical systems is to try to classify Anosov flows up to orbit-equivalence. This question is particularly interesting in dimension 3 where we both have lots of examples and a rich, but still poorly understood, relationships between the dynamics of the flow and the topology of the manifold. By a result of T. Barbot, classifying Anosov flows (or more general pseudo-Anosov flows) in dimension 3 up to orbit equivalence restricts to classifying, up to conjugacy, certain actions of \pi_1(M) on the orbit space, a topological plane with two transverse foliations.

In this talk, I will recall the above and discuss a new complete invariant for transitive (pseudo)-Anosov flows which often reduces to just knowing which conjugacy classes in \pi_1(M) are represented by periodic orbits of the flow.

If time permits, I’ll talk about some applications with link to contact geometry. This is all joint work with Kathryn Mann, Steven Frankel and Sergio Fenley.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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