A note on the transfer map.
A propos de conjectures de Serre et Sullivan.
À propos d'un théorème de Charles Ehresmann sur les feuilletages
A Pullback theorem for cofibrations.
A Pullback Theorem for Locally-Equiconnected Spaces.
A Remark on "Homotopy Fibrations".
A remark on the Chern class of a tensor product.
A Remark on Universal Connections.
A splitting principle for group representations.
A Universal Proper G-Space.
A universal space for normal bundles of n-manifolds.
Abstract tangent functors
Adjunction of n-equivalences and triad connectivity.
We prove a new adjunction theorem for n-equivalences. This theorem enables us to produce a simple geometric version of proof of the triad connectivity theorem of Blakers and Massey. An important intermediate step is a study of the collapsing map S∨X → S, S being a sphere.
Algebraic characteristic classes for idempotent matrices.
This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.
Algebraic realization of equivariant vector bundles.
Algebroid nature of the characteristic classes of flat bundles
The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4], or the...
An acyclic extension of the braid group.
An algebraic model of fibration with the fiber -space.
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
An approach to shape covering maps.
In this note we give an approach to shape covering maps which is comparable to that of *-fibrations (Mardesic and Rushing (1978)). The introduced notion conserves some important properties of usual covering maps.