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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)

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 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 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)

- 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)

- William M Goldman, François Labourie
- 2012

Dedicated to the memory of Dan Rudolph Abstract. Let M 3 be a Margulis spacetime whose associated complete hyperbolic surface 2 has a compact convex core. Generalizing the correspondence between closed geodesics on M 3 and closed geodesics on 2 , we establish an orbit equivalence between recurrent spacelike geodesics on M 3 and recurrent geodesics on 2. In… (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)

- William M Goldman, Richard A Wentworth
- 2004

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichmüller space T S which is a qualitative invariant of the holonomy representation ρ of π 1 (S). Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function E ρ is proper for any convex… (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)

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)