Teichmuller
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Billiards and Teichmuller curves - Harvard University
people.math.harvard.eduBilliards and Teichmuller curves. McMullen24 October 2021AbstractA Teichmuller curve V Mg is an isometrically immersed al-gebraic curve in the. moduli space of Riemann surfaces. These rare, extremal objects are related to billiards in polygons, Hodge theory, algebr.
Introduction to Teichmuller¨ theory - IMJ-PRG
webusers.imj-prg.frThe Teichmuller¨ space of a surface Sis the deformation space of complex structures on S and can also be seen as a space of hyperbolic metrics on S. The aim of this course will be to study the geometry and topology of this space and its quotient: the moduli space of Riemann surfaces.
TEICHMULLER THEORY AND HYPERBOLIZATION OF THREE …
math.uchicago.eduTeichmuller theory, and then demonstrate how Teichmuller theory paves the way for Thurston’s Hyperbolization Theorem, a remarkable theorem relating 3-manifold topology to hyperbolic geometry. The general Hyperbolization Theorem states that a compact, irreducible, atoroidal 3-manifold always admits a complete hyperbolic metric of nite volume.
Teichmu¨ller Theory Notes - Harvard University
people.math.harvard.eduThe 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.
Introduction to Teichmu¨ller Theory - UC Davis
www.math.ucdavis.edu12 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 ∈.