#### Filter Results:

- Full text PDF available (62)

#### Publication Year

1967

2016

- This year (0)
- Last 5 years (5)
- Last 10 years (29)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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 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 2form. 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)

where B : E x E —• E' is a bilinear map and E' is a vector space. (E may be identified with the Zariski tangent space to Q at 0.) Let V be an algebraic variety and x € V be a point. We say that V is quadratic at x if the analytic germ of V at x is equivalent to the germ of a quadratic cone at 0. Let T be a finitely generated group and G a k-algebraic group.… (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 algebraic group over R [3, 18, 27, 32]. The group G acts on Hom(Tr, G) by conjugation and the orbit space will be denoted by Horn(n, G)/G. Geometrically, the G-orbits on… (More)

is isomorphic to PGL(2,Z)⋉ (Z/2⊕ Z/2). For t ∈ R , the Γ-action on κ(t) ∩ R displays rich and varied dynamics. The action of Γ preserves a Poisson structure defining a Γ–invariant area form on each κ(t) ∩ R . For t < 2, the action of Γ is properly discontinuous on the four contractible components of κ(t) ∩R and ergodic on the compact component (which is… (More)

The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension

- Suhyoung Choi, William M. Goldman, SUHYOUNG CHOI
- 2008

he deformation space t(E) of convex Rp2_ structures on a closed surface Y with X(z) < 0 is closed in the space Hom(7r, SL(3, IR))/SL(3, IR) of equivalence classes of representations r1 (l) -SL(3, IR) . Using this fact, we prove Hitchin's conjecture that the contractible "Teichmuller component" (Lie groups and Teichmuller space, preprint) of Hom(7r, SL(3,… (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)

We construct actions of fundamental groups of Riemann surfaces by automorphisms of the complex hyperbolic plane, which realize all possible values of Toledo's invariant. For integer values of these actions are discrete embeddings. The quotient complex hyperbolic surfaces are disc bundles over Riemann surfaces, whose topological type is determined in terms… (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