The intrinsic asymmetry and inhomogeneity of Teichmüller space
نویسندگان
چکیده
Let S = Sg,n be a connected, orientable surface of genus g ≥ 0 with n ≥ 0 punctures. Let Teich(S) denote the corresponding Teichmüller space, and let Mod(S) denote the mapping class group of S. Understanding the analogy of Teich(S) with symmetric spaces is a wellknown theme. Recall that a complete Riemannian manifold X is symmetric if it is symmetric at each point x ∈ X: the map γ(t) 7→ γ(−t) which flips geodesics about x is an isometry. Symmetric spaces X are homogeneous: the isometry group Isom(X) acts transitively on X. In his famous paper [Ro], Royden studied the possible symmetry and homogeneity of Teich(S), endowed with the Teichmüller metric.
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