三维阿诺索夫流的泰希米勒空间
The Teichmüller Space of a 3-Dimensional Anosov Flow
AI总结：
本文研究三维阿诺索夫流的泰希米勒空间，通过光滑轨道等价类将其表示为两个函数空间的乘积，并证明了三维可传递阿诺索夫流轨道等价空间的路径连通性，同时展示了其与微分同胚群的同伦等价关系。
摘要：
对于在三维闭流形M上可传递的阿诺索夫流Φ，我们将其泰希米勒空间（在光滑轨道等价类的意义下）表示为两个函数空间的乘积。作为应用，我们证明了三维可传递阿诺索夫流的轨道等价空间的路径连通性，从而回答了Potrie在三维情况下的问题1的肯定答案。进一步，在M上的C^r光滑（r≥1）三维阿诺索夫流空间中，我们证明包含Φ的A^r(Φ)路径分量与流形的微分同胚群的身份分量同伦等价，即A^r(Φ) ≃ Diff^r_0(M)。此外，我们还证明了三维可传递阿诺索夫流在具有C^1光滑强稳定叶状结构时时间保持共轭的刚性，从而部分回答了Gogolev-Leguil-Rodriguez Hertz的问题2.8。
英文摘要：
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].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
