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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)
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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)
T T T T T T T T T T T T T T T Abstract The group Γ of automorphisms of the polynomial κ(x, y, z) = x 2 + y 2 + z 2 − xyz − 2 is isomorphic to PGL(2, Z) ⋉ (Z/2 ⊕ Z/2). For t ∈ R, the Γ-action on κ −1 (t) ∩ R 3 displays rich and varied dynamics. The action of Γ preserves a Poisson structure defining a Γ–invariant area form on each κ −1 (t) ∩ R 3. For t < 2,(More)