Anosov flows in dimension 3: an outside look

Abstract

These notes were intended as support material for a minicourse on Anosov flows in the conference "Symplectic geometry and Anosov flows'' which took place in Heidelberg in July 2024 organized by Peter Albers, Jonathan Bowden and Agust\'in Moreno. I took the invitation to present the subject as asking from an outsider view of the subject, given the fact that my research uses both ideas and results from the theory of Anosov flows. The point of view of the course is to provide an overview of the main results and questions in the subject, with emphasis on the interaction with topology, geometry, specially symplectic geometry and contact aspects of the theory. Some detail is given in the presentation of the Barbot-Fenley theory of leaf spaces. Hopefully the notes will contribute in gaining a working knowledge of the theory and its many beautiful connections.