Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
A uniqueness theorem for transitive Anosov flows obtained by gluing hyperbolic plugs

François Béguin and Bin Yu

Algebraic & Geometric Topology 23 (2023) 2673–2713

In work with C Bonatti, we defined a general procedure to build new examples of Anosov flows in dimension 3. The procedure consists in gluing together some building blocks, called hyperbolic plugs, along their boundary in order to obtain a closed three-manifold endowed with a complete flow. The main theorem of that work states that (under some mild hypotheses) it is possible to choose the gluing maps so the resulting flow is Anosov. Here we show a uniqueness result for Anosov flows obtained by such a procedure. Roughly speaking, we show that the orbital equivalence class of these Anosov flows is insensitive to the precise choice of the gluing maps used in the construction. The proof relies on a coding procedure, which we find interesting for its own sake, and follows a strategy that was introduced by T Barbot in a particular case.

Anosov flows, hyperbolic plugs, orbitally equivalent, flows on three-dimensional manifolds
Mathematical Subject Classification
Primary: 37D20
Secondary: 57M99
Received: 13 January 2021
Revised: 3 December 2021
Accepted: 14 January 2022
Published: 7 September 2023
François Béguin
LAGA, UMR 7539 du CNRS
Université Sorbonne Paris Nord
Bin Yu
School of Mathematical Sciences
Tongji University

Open Access made possible by participating institutions via Subscribe to Open.