(bi)-Foliations of the plane and laminations of the circle

Abstract: A "bifoliation" of a two-dimensional space is a way of covering it with local charts to the Euclidean plane R^2 so that overlap maps in R^2 match up the vertical and horizontal coordinate directions. Such objects arise naturally in many dynamical contexts such as Anosov diffeomorphisms on surfaces, or flows on 3-manifolds. A trick due to Mather lets one compactify a bifoliated plane with a "circle at infinity" using the data of the bifoliation. In recent work with Barthelmé and Bonatti, we studied the inverse question: what is the minimum amount of data from infinity that allows one to reverse this procedure and uniquely reconstruct a bifoliation of the plane? This talk will explain the answer! While our motivation for this question was the problem of classifying pseudo-Anosov flows, the problem and solution are entirely in the realm of low-dimensional topology.

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

Audience: researchers in the topic

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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