Year: 2025
Type: article
Abstract: Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs.We show a similar correspondence between projectively Anosov flows and bicontact structures, extending the work of Mitsumatsu and Eliashberg-Thurston.As a consequence, every Anosov flow on a closed oriented three-manifold M gives rise to a Liouville structure on R M which is well-defined up to homotopy, and which only depends on the homotopy class of the Anosov flow.Our results also provide a new perspective on the classification problem of Anosov flows in dimension three.53E50, 57K33, 57K43; 37D20, 37D30 1. Introduction 1793 2. Anosov Liouville pairs 1800 3. From Anosov flows to Anosov Liouville pairs and back 1805 4. Spaces of Anosov Liouville pairs and bicontact structures 1817 5. Linear Liouville pairs 1825 Appendix A. Smoothing lemmas 1832
Source: Algebraic & Geometric Topology
Author: Thomas Massoni
Institutions: Princeton University, Stanford University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411625092