Seminar

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 In 1936 Ch. Ehresmann raised the question of ``classification'' of geometric structures modeled on a "classical geometry" (such as projective geometry) on a fixed topological manifold. An example is the classification of Euclidean structures (flat Riemannian metrics) on the n-torus, where the moduli space is naturally the biquotient GL(n,Z)\Gl(n,R)/O(n). By an observation of Thurston this problem intimately relates to the analogous problem of ``classifying'' representations of the fundamental group. This leads to interesting dynamical systems which are of interest in their own right. In this talk I will survey this subject with examples to illustrate the richness and depth of this theory.