In [7] it was shown that if n is the fundamental group ofa closed oriented surface S and G is Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes ofâ€¦ (More)

A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metricâ€¦ (More)

The group Î“ of automorphisms of the polynomial (x; y; z) = x + y + z âˆ’ xyz âˆ’ 2 is isomorphic to PGL(2;Z)n (Z=2 Z=2): For t 2 R , the Î“-action on âˆ’1(t) \ R displays rich and varied dynamics. Theâ€¦ (More)

Since rt is a finitely generated group, the space Hom0r, G) is a real analytic variety whenever G is a connected Lie group, and is a real affine algebraic variety whenever G is a linear algebraicâ€¦ (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

The space of inequivalent representations of a compact surface S with Ï‡(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell ofâ€¦ (More)

Those groups r which act properly discontinuously and aillnely on II?â€™ with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finiteâ€¦ (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 beâ€¦ (More)

Deformation spaces Hom(Ï€, G)/G of representations of the fundamental group Ï€ of a surface Î£ in a Lie group G admit natural actions of the mapping class group ModÎ£, preserving a Poisson structure.â€¦ (More)