Orbit equivalences of ℝ–covered Anosov flowsand hyperbolic-like actions on the line
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Bibliographic record
Abstract
We prove a rigidity result for group actions on the line whose elements have what we call "hyperboliclike" dynamics.Using this, we give a rigidity theorem for R-covered Anosov flows on 3-manifolds, characterizing orbit equivalent flows in terms of the elements of the fundamental group represented by periodic orbits.As consequences of this, we give an efficient criterion to determine the isotopy classes of self-orbit equivalences of R-covered Anosov flows, and prove finiteness of contact Anosov flows on any given manifold.In the appendix, with Jonathan Bowden, we prove that orbit equivalences of contact Anosov flows correspond exactly to isomorphisms of the associated contact structures.This gives a powerful tool to translate results on Anosov flows to contact geometry and vice versa.We illustrate its use by giving two new results in contact geometry: the existence of manifolds with arbitrarily many distinct Anosov contact structures, answering a question of Foulon, Hasselblatt and Vaugon, and a virtual description of the group of contact transformations of a Anosov contact structure, generalizing a result of Giroux and Massot.37D20, 57M60
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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