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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)

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)

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)

- DE L’I.H.É.S, 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)

- Suhyoung Choi, William M. Goldman, SUHYOUNG CHOI
- 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)

- Robert L. Benedetto, William M. Goldman
- Experimental Mathematics
- 1999

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)

The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP 2 by a properly dis-continuous group of projective transformations is a cell of dimension The purpose of this paper is to investigate convex real projective structures on compact surfaces. Let RP 2 be the real projective plane and PGL(3, R)… (More)

Let M be a compact surface with (M) < 0 and let G be a compact Lie group whose Levi factor is a product of groups locally isomorphic to SU(2) (for example SU(2)). Then the map

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)