A better proof of the Goldman-Parker conjecture.
A class of tight contact structures on .
A criterion for homeomorphism between closed Haken manifolds.
A filtration of the set of integral homological 3-spheres.
A geometric study of Fibonacci groups.
A new algorithm for recognizing the unknot.
A new invariant on hyperbolic Dehn surgery space.
A Note on Hyperbolic 3-Manifolds of the Same Volume.
A proof of Reidemeister-Singer’s theorem by Cerf’s methods
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
A trace-class rigidity theorem for Kleinian groups.
Actions of discrete groups on nonpositively curved spaces.
Alexander polynomial, finite type invariants and volume of hyperbolic knots.
Algorithmic detection and description of hyperbolic structures on closed 3-manifolds with solvable word problem.
All flat manifolds are cusps of hyperbolic orbifolds.
All integral slopes can be Seifert fibered slopes for hyperbolic knots.
All roots of unity are detected by the A-polynomial.
An algorithm to detect laminar 3-manifolds.
An asymptotic formula for the eta invariants of hyperbolic 3-manifolds.
An irreducible Heegaard diagram of the real projective 3-space .
Andreev’s Theorem on hyperbolic polyhedra
In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that the resulting...