Disjonction de sous-variétés et application au croisement des anses
In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
Un des problèmes historiques de la théorie homotopique des espaces est de mesurer l’effet de l’attachement d’une cellule au niveau des groupes d’homotopie. Le problème de l’attachement inerte reste en particulier un problème ouvert. Nous donnons ici une réponse partielle à ce problème.
We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite CW-complexes;...
If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting...