Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, II : Branching foliations

Barthelmé, Thomas¹ ; Fenley, Sérgio R² ; Frankel, Steven³ ; Potrie, Rafael⁴

¹ Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada
² Department of Mathematics, Florida State University, Tallahassee, FL, United States
³ Department of Mathematics, Washington University in St. Louis, St Louis, MO, United States
⁴ Facultad de Ciencias – Centro de Matemática, Universidad de la República, Montevideo, Uruguay

Geometry & topology, Tome 27 (2023) no. 8, pp. 3095-3181.

Résumé

We study $3$–dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov’s center stable and center unstable branching foliations. This extends our previous study of the true foliations that appear in the dynamically coherent case. We complete the classification of such diffeomorphisms in Seifert fibered manifolds. In hyperbolic manifolds, we show that any such diffeomorphism is either dynamically coherent and has a power that is a discretized Anosov flow, or is of a new potential class called a double translation.

Détail

DOI : 10.2140/gt.2023.27.3095

Keywords: partial hyperbolicity, 3–manifolds, foliations

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