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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)

A symplectic structure on a manifold is a closed nondegenerate exterior 2-form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures: the Jacobi variety, Teichmiiller space, moduli spaces of stable… (More)

Let S be a closed oriented surface of genus g > 1 and let ~r denote its fundamental group. Let G be a semisimple Lie group. The purpose of this paper is to investigate the global properties of the space Hom(rc, G) of all representations n~G, when G is locally isomorphic to either PSL(2, C) or PSL(2, R). The main results of this paper may be summarized as… (More)

- William M Goldman, John J Millson
- 2003

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)

Those groups r which act properly discontinuously and aillnely on II?' with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finite index, thus establishing a conjecture of Auslander in dimension three. Then unimodular simply transitive alTine actions on IR' are classified; this leads to a… (More)

- Suhyoung Choi, William M Goldman
- 2008

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that… (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)

Deformation spaces Hom(π, G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group Mod Σ , preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the associated deformation space contains open subsets containing the… (More)

- W Goldman, F Labourie, G Margulis
- 2004

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)

Many interesting geometric structures on manifolds can be interpreted as structures locally modelled on homogeneous spaces. Given a homogeneous space (X, G) and a manifold M , there is a deformation space of structures on M locally modelled on the geometry of X invariant under G. Such a geometric structure on a manifold M determines a representation (unique… (More)