The Teichmuller Space of a 3-Dimensional Anosov Flow

Speaker：Yi Shi (Sichuan University)

Time：2026-9-7 16:00

Location：Conference Room S208 at Experiment Building at Haiyun Campus

Abstract:

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 in dimension 3. Further, in the space of C^r-smooth 3-dimensional Anosov flows on M, we show that the path component containing this flow is homotopy equivalent to the identity component of the diffeomorphism group of the manifold. This is a joint work with R. Gu.