Conjugacy classes of the hyperelliptic mapping class group of genus 2 and 3.
Constructing conformally flat structures on some Seifert fibred 3-manifolds.
Constructing equivariant maps for representations
We show that if is a discrete subgroup of the group of the isometries of , and if is a representation of into the group of the isometries of , then any -equivariant map extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable -equivariant...
Constructing symplectic forms on 4--manifolds which vanish on circles.
Constructing taut foliations.
Contact 3-manifolds twenty years since J. Martinet's work
The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on . Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on .
Contact geometry and complex surfaces.
Contact topology and the structure of 5-manifolds with
We prove a structure theorem for closed, orientable 5-manifolds with fundamental group and second Stiefel-Whitney class equal to zero on . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain -quotients of .
Counting immersed surfaces in hyperbolic 3-manifolds.
Cusp structures of alternating links.
Cyclic branched coverings and homology 3-spheres with large group actions
We show that, if the covering involution of a 3-manifold M occurring as the 2-fold branched covering of a knot in the 3-sphere is contained in a finite nonabelian simple group G of diffeomorphisms of M, then M is a homology 3-sphere and G isomorphic to the alternating or dodecahedral group 𝔸₅ ≅ PSL(2,5). An example of such a 3-manifold is the spherical Poincaré sphere. We construct hyperbolic analogues of the Poincaré sphere. We also give examples of hyperbolic ℤ₂-homology 3-spheres with PSL(2,q)-actions,...
Cyclic branched coverings of 2-bridge knots.
In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.
Cylinder and horoball packing in hyperbolic space.
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.