Invariants of Three-dimensional Manifolds.
Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations.
Invariants of translation surfaces
We definite invariants of translation surfaces which refine Veech groups. These aid in exact determination of Veech groups. We give examples where two surfaces of isomorphic Veech group cannot even share a common tree of balanced affine coverings. We also show that there exist translation surfaces of isomorphic Veech groups which cannot affinely cover any common surface. We also extend a result of Gutkin and Judge and thereby give the first examples of noncompact Fuchsian...
Invariants on three-manifolds with spin structure.
Involutions in mapping class groups of non-orientable surfaces.
We prove that the mapping class group and the pure mapping class group of closed non-orientable surfaces with punctures are generated by involutions.
Involutions of 3-dimensional handlebodies
We study the orientation preserving involutions of the orientable 3-dimensional handlebody , for any genus g. A complete classification of such involutions is given in terms of their fixed points.
Isometric Embeddings of Pro-Euclidean Spaces
In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...
Isotopie de formes fermées en dimension trois.
Iteration on Teichmüller space.
Jones polynomials, volume and essential knot surfaces: a survey
This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.
Klein Hyperbottle
Knot and link projections in 3-manifolds.
Knot manifolds with isomorphic spines
We study the relation between the concept of spine and the representation of orientable bordered 3-manifolds by Heegaard diagrams. As a consequence, we show that composing invertible non-amphicheiral knots yields examples of topologically different knot manifolds with isomorphic spines. These results are related to some questions listed in [9], [11] and recover the main theorem of [10] as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors completes...
Knots with property .
Knotted Lattice-Like Space Fillers.
Kurven auf orientierbaren Flächen.
La conjecture de Poincaré topologique en dimension 4
La courbure totale absolue minimale des surfaces dans
La décomposition dynamique et la différentiabilité des feuilletages des surfaces
Soit un feuilletage singulier d’une surface compacte . Pour analyser la dynamique de , on décompose de façon canonique en sous-surfaces bordées par des courbes transverses à : les composantes de la récurrence de (ensembles quasiminimaux) sont contenues dans les “régions de récurrence” et peuvent être étudiées séparément; par contre dans les autres régions, dites “régions de passage”, la dynamique est triviale. On propose ensuite une définition des feuilletages singuliers de classe sur...
La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie