PreprintCC BY-NC 4.0HAL
Exotic codimension one Anosov flows
Abstract
We construct Anosov flows in certain circle bundles over closed hyperbolic 3-manifolds, producing counterexamples to a conjecture of Verjovsky. Some of these 4-manifolds admit infinitely many distinct Anosov flows up to orbit equivalence. The construction is made by using Cannon-Thurston maps associated to pseudo-Anosov quasigeodesic flows in hyperbolic 3-manifolds.
Related
- Codimension-one holomorphic Anosov diffeomorphisms
- Finiteness of Anosov and pseudo-Anosov flows on hyperbolic 3-manifolds
- Klingenberg's theorem on Anosov geodesic flows
- Construction of Anosov flows on fibered hyperbolic 3-manifolds
- Rigidity from the strong unstable foliation for higher-dimensional Anosov and partially hyperbolic flows
BibTeX
@misc{fenley2026exotic,
title = {{Exotic codimension one Anosov flows}},
author = {Sergio Fenley and Kathryn Mann and Rafael Potrie},
howpublished = {HAL},
year = {2026},
month = may,
eprint = {2605.25082},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05838011v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Exotic codimension one Anosov flows
AU - Sergio Fenley
AU - Kathryn Mann
AU - Rafael Potrie
PY - 2026
DA - 2026/05/24
PB - HAL
UR - https://hal.science/hal-05838011v1
AB - We construct Anosov flows in certain circle bundles over closed hyperbolic 3-manifolds, producing counterexamples to a conjecture of Verjovsky. Some of these 4-manifolds admit infinitely many distinct Anosov flows up to orbit equivalence. The construction is made by using Cannon-Thurston maps associated to pseudo-Anosov quasigeodesic flows in hyperbolic 3-manifolds.
ER -