Deformations of representations of discrete subgroups of SO (3,1).
Degree one maps between small 3-manifolds and Heegaard genus.
Dehn filling: A survey
In this paper we give a brief survey of the present state of knowledge on exceptional Dehn fillings on 3-manifolds with torus boundary. For our discussion, it is necessary to first give a quick overview of what is presently known, and what is conjectured, about the structure of 3-manifolds. This is done in Section 2. In Section 3 we summarize the known bounds on the distances between various kinds of exceptional Dehn fillings, and compare these with the distances that arise in known examples. In...
Dehn twists on nonorientable surfaces
Let be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...
Démonstration d'un théorème de Penner sur la composition des twists de Dehn
Discrete -groups with a parabolic generator.
Distances of Heegaard splittings.
Dynamical systems and the homology norm of a 3-manifold II.
Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation
We consider representations of the fundamental group of the four punctured sphere into . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from -representations. We prove the absence of invariant affine structure (and invariant...