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In [7] it was shown that if n is the fundamental group of a closed oriented surface S and G is Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representation n-+G has a natural symplectic structure. This symplectic structure generalizes the Weil-Petersson Kahler form on Teichmiiller space (taking G= PSL(2,(More)
The deformation theory of representations of fundamental groups of compact Kähler manifolds Publications mathématiques de l'I. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques Abstract. — Let F be the fundamental group of a compact Kahler manifold M and let G be a real algebraic Lie group. Let 9l(r, G) denote the(More)
Let M be a quadruply-punctured sphere with boundary components A; B; C; D. The SL(2; C)-character variety of M consists of equivalence classes of homomorphisms of 1 (M) ?! SL(2; C) and can be identiied with a quartic hypersurface in C 7. corresponding to representations with tr((A)) = a, tr((B)) = b, tr((C)) = c, tr((D)) = d is a cubic surface in C 3. We(More)
Let Γ 0 ⊂ O(2, 1) be a Schottky group, and let Σ = H 2 /Γ 0 be the corresponding hyperbolic surface. Let C(Σ) denote the space of geodesic currents on Σ. The cohomology group H 1 (Γ 0 , V) parametrizes equivalence classes of affine deformations Γ u of Γ 0 acting on an irreducible representation V of O(2, 1). We define a continuous biaffine map C(Σ) × H 1 (Γ(More)