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Introduction to Teichmu¨ller Theory - UC Davis

Introduction to Teichmu¨ller Theory - UC Davis

www.math.ucdavis.edu

12 Teichm ̈uller theory from the Kodaira-Spencer point of view. Definition (Kodaira- Spencer): A holomorphic family is a complex manifold V = V m+1 and a holomorphic map π : V → M = Mm where Mm is a complex manifold and all preimages π−1(t) are Riemann surfaces (t M). In our case, M = Φ(T (X)) ⊂ Q(X) and ∈.

  Introduction, Theory, Llers, Teichmu, Introduction to teichmu, 168 ller theory

Teichmu¨ller Theory Notes - Harvard University

Teichmu¨ller Theory Notes - Harvard University

people.math.harvard.edu

The integral geometric measure on G is defined as follows. Fix an oriented geodesic γ ⊂ H. Then there is an injective map (x, θ) to the unique unoriented geodesic δ(x, θ) through γ × S1 → G sending. x making angle θ with γ. (Since the geodesics are unoriented, θ ranges in [0, π].) The measure = (1/2) sin θdθ dx.

  Notes, Theory, Llers, Teichmu, 168 ller theory notes

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Introduction to Teichmu¨ller Theory, Teichmu¨ller Theory Notes