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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.
Béguin, François 1 ; Yu, Bin 2
@article{10_2140_agt_2023_23_2673,
author = {B\'eguin, Fran\c{c}ois and Yu, Bin},
title = {A uniqueness theorem for transitive {Anosov} flows obtained by gluing hyperbolic plugs},
journal = {Algebraic and Geometric Topology},
pages = {2673--2713},
publisher = {mathdoc},
volume = {23},
number = {6},
year = {2023},
doi = {10.2140/agt.2023.23.2673},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2673/}
}
TY - JOUR AU - Béguin, François AU - Yu, Bin TI - A uniqueness theorem for transitive Anosov flows obtained by gluing hyperbolic plugs JO - Algebraic and Geometric Topology PY - 2023 SP - 2673 EP - 2713 VL - 23 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2673/ DO - 10.2140/agt.2023.23.2673 ID - 10_2140_agt_2023_23_2673 ER -
%0 Journal Article %A Béguin, François %A Yu, Bin %T A uniqueness theorem for transitive Anosov flows obtained by gluing hyperbolic plugs %J Algebraic and Geometric Topology %D 2023 %P 2673-2713 %V 23 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2673/ %R 10.2140/agt.2023.23.2673 %F 10_2140_agt_2023_23_2673
Béguin, François; Yu, Bin. A uniqueness theorem for transitive Anosov flows obtained by gluing hyperbolic plugs. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2673-2713. doi: 10.2140/agt.2023.23.2673
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