On H-spaces over a base space.
On Poincaré 3-Complexes with Binary Polyhedral Fundamental Group.
On shape and fundamental deformation retracts
On shape and fundamental deformation retracts II
On spaces of the same strong -type.
On the 2-type of an iterated loop space.
On the genus of finite CW-H-spaces
On the group of homotopy equivalences of simply connected five manifolds.
On the homotopy equivalence of the spaces of proper and local maps
We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.
On the kernel of holonomy.
A connection on a principal G-bundle may be identified with a smooth group morphism H : GL∞(M) → G, called a holonomy, where GL∞(M) is a group of equivalence classes of loops on the base M. The present article focuses on the kernel of this morphism, which consists of the classes of loops along which parallel transport is trivial. Use is made of a formula expressing the gauge potential as a suitable derivative of the holonomy, allowing a different proof of a theorem of Lewandowski’s, which states...
On the Self-Equivalences of a Space with Non-cyclic Fundamental Group.
Polyhedra with virtually polycyclic fundamental groups have finite depth
The notions of capacity and depth of compacta were introduced by K. Borsuk in the seventies together with some open questions. In a previous paper, in connection with one of them, we proved that there exist polyhedra with polycyclic fundamental groups and infinite capacity, i.e. dominating infinitely many different homotopy types (or equivalently, shapes). In this paper we show that every polyhedron with virtually polycyclic fundamental group has finite depth, i.e., there is a bound on the lengths...
Power-cancellation of CW-complexes with few cells.
In this paper we use the fact that the rings of integer matrices have the power-substitution property in order to obtain a power-cancellation property for homotopy types of CW-complexes with one cell in dimensions 0 and 4n and a finite number of cells in dimension 2n.
Pullback and pushout squares in a special double category with connection
Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types.
Rational nilpotent groups as subgroups of self-homotopy equivalences
Rationale Homotopietypen.
Realization Problems for the Group of Homotopy Classes of Self-Equivalences.
Représentation des groupes d'extension. Applications
Rétractes d'un espace
Notre but dans ce texte est de montrer le résultat suivant : Si est un C.W. complexe, simplement connexe, de type fini, avec finiment engendré comme algèbre de Lie, alors, à équivalence d’homotopie rationnelle près, il n’existe qu’un nombre fini de rétractes de . L’existence d’un nombre fini de rétractes a été obtenue par L. Renner en 1990 dans le cas où est finiment engendré en tant que -algèbre. Notre résultat élargit ainsi le cadre des espaces n’ayant, à équivalence d’homotopie rationnelle...