Invariants de Vassiliev des nœuds
Invariants for Lagrangian tori.
Invariants from triangulations of hyperbolic 3-manifolds.
Invariants homotopiques attachés aux fibrés symplectiques
On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne -orientée dans : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré -symplectique, c’est-à-dire dont le groupe structural est le revêtement à feuillets de . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...
Invariants in contact topology.
Invariants of 3-manifolds via link polynomials and quantum groups.
Invariants of -type links via an extension of the Kauffman bracket.
Invariants of branched covering from the work of Serre and Mumford.
Invariants of piecewise-linear knots
We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.
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.
Inverse limits of simplicial complexes
Invertible Amphicheiral Knots.
Invertible Knot Cobordisms
Invertible polynomial mappings via Newton non-degeneracy
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.
Inviluppi di olomorfia e gruppi di coomologia di Hausdorff
Involutions Fixing and arbitraty product of spheres and a point.
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.