The Teichmüller Space of a 3-Dimensional Anosov Flow
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918442130472960 |
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| author | Gu, Ruihao Shi, Yi |
| author_facet | Gu, Ruihao Shi, Yi |
| contents | For a transitive Anosov flow $Φ$ on 3-dimensional closed manifold $M$ , we realize its Teichmüller space in the sense of smooth orbit-equivalence classes as a product of two function spaces. As an application, we show the path-connectedness of the orbit-equivalence space of 3-dimensional transitive Anosov flows which gives a positive answer of Potrie [53, Question 1] in dimension 3. Further, in the space of $C^r$-smooth ($r\geq 1$) 3-dimensional Anosov flows on $M$, we show that $\mathcal{A}^r(Φ)$ the path component containing $Φ$ is homotopy equivalent to the identity component of the diffeomorphism group of the manifold, namely, \[ \mathcal{A}^r(Φ)\simeq {\rm Diff}^r_0(M). \] Moreover, we show the rigidity of time-preserving conjugacy for 3-dimensional transitive Anosov flows admitting $C^1$-smooth strong stable foliations, which gives partial answer of Gogolev-Leguil- Rodriguez Hertz [27, Question 2.8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04249 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Teichmüller Space of a 3-Dimensional Anosov Flow Gu, Ruihao Shi, Yi Dynamical Systems 37C15, 37C10, 37D20 For a transitive Anosov flow $Φ$ on 3-dimensional closed manifold $M$ , we realize its Teichmüller space in the sense of smooth orbit-equivalence classes as a product of two function spaces. As an application, we show the path-connectedness of the orbit-equivalence space of 3-dimensional transitive Anosov flows which gives a positive answer of Potrie [53, Question 1] in dimension 3. Further, in the space of $C^r$-smooth ($r\geq 1$) 3-dimensional Anosov flows on $M$, we show that $\mathcal{A}^r(Φ)$ the path component containing $Φ$ is homotopy equivalent to the identity component of the diffeomorphism group of the manifold, namely, \[ \mathcal{A}^r(Φ)\simeq {\rm Diff}^r_0(M). \] Moreover, we show the rigidity of time-preserving conjugacy for 3-dimensional transitive Anosov flows admitting $C^1$-smooth strong stable foliations, which gives partial answer of Gogolev-Leguil- Rodriguez Hertz [27, Question 2.8]. |
| title | The Teichmüller Space of a 3-Dimensional Anosov Flow |
| topic | Dynamical Systems 37C15, 37C10, 37D20 |
| url | https://arxiv.org/abs/2602.04249 |