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NCTS Differential Geometry Seminar
16:00 - 17:00, May 16, 2017 (Tuesday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Entropy, Critical Exponent, and Immersed Surfaces in Hyperbolic 3-Manifolds
Lien-Yung Gao (University of Notre Dame & University of Chicago)


Consider a π1-injective immersion f:S→Mfrom a compact surface S to a hyperbolic 3-manifold (M,h). Let Γ denote the copy of π1(S) in Isom(H3) induced by the immersion. In this talk, I will discuss relations between two dynamics quantities: the critical exponent δ(Γ) and the topological entropy htop(S) of the geodesic flow for the immersed surface (S,f*h). These dynamics relations lead us to geometry results: through these relations, one can characterize certain hyperbolic 3-manifolds such as Fuchsian manifolds, quasi-Fuchsian manifolds, and almost-Fuchsian manifolds. If time permits, I will also discuss applications of these relations to the moduli space of S introduced by C. Taubes.


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