Theorem on signatures
Théorèmes de dualité pour les faisceaux algébriques cohérents
Théorèmes de fibration des espaces de plongements. Applications
Théorie de jauge et symétries des fibrés
Soit un -fibré principal différentiable sur une variété ( un groupe de Lie compact). Étant donné une action d’un groupe de Lie compact sur , on se pose la question de savoir si elle provient d’une action sur le fibré . L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de que l’on induit naturellement sur divers espaces de modules de -connexions sur .
Théorie de Smith algébrique et classification des --injectifs
Théorie des opérades de Koszul et homologie des algèbres de Poisson
Théorie du degré dans certains espaces de Fréchet d'après R. S. Hamilton
Théorie homotopique des groupes de Lie
Théories cohomologiques.
There Are No Essential Phantom Mappings from 1-dimensional CW-complexes
A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom...
There are no Phantom Pairs of Mappings to 1-Dimensional CW-Complexes
Two mappings from a CW-complex to a 1-dimensional CW-complex are homotopic if and only if their restrictions to finite subcomplexes are homotopic.
There exists a polyhedron dominating infinitely many different homotopy types
T-homotopy and refinement of observation. III. Invariance of the branching and merging homologies.
T-homotopy and refinement of observation. IV. Invariance of the underlying homotopy type.
Three questions of Borsuk concerning movability and fundamental retraction
Three themes in the work of Charles Ehresmann: local-to-global; groupoids; higher dimensions
This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.
Toda Brackets in Differential Topology
Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...
Topological and approximation methods of degree theory of set-valued maps [Book]
Topological bar-codes of fractals: a new characterization of symmetric binary fractal trees
The goal of this paper is to provide foundations for a new way to classify and characterize fractals using methods of computational topology. The fractal dimension is a main characteristic of fractal-like objects, and has proved to be a very useful tool for applications. However, it does not fully characterize a fractal. We can obtain fractals with the same dimension that are quite different topologically. Motivated by techniques from shape theory and computational topology, we consider fractals...