Generalized classes of groups, C-nilpotent spaces and "The Hurewicz theorem".
Gradient otopies of gradient local maps
We introduce various classes of local maps: gradient, gradient-like, proper etc. We prove Parusiński's theorem for otopy classes of gradient local maps.
Group Extensions and Principal Fibrations.
Groupoids and crossed objects in algebraic topology.
Groupoids, stability cokernel sequences and duality
Gruppen von Homotopieklassen von Abbildungen in Produkte von Eilenberg-Maclane-Räumen.
Higher homotopy groupoids and Toda brackets.
Homology and homotopy groups of the complement of certain family of fibers in a critical point problem.
Homology Equivalences and a Technique of Ganea.
Homotopie de l'espace des équivalences d'homotopie fibrées
On construit une suite spectrale qui converge vers le bigradué associé à une filtration convenable des groupes d’homotopie du monoïde simplicial des équivalences d’homotopie fibrées d’un fibré de Kan dans lui-même. On obtient de nouveaux calculs de ces groupes. En particulier, on calcule le groupe des classes d’homotopie des équivalences d’homotopie d’un espace ayant trois groupes d’homotopie non nuls en dessous de sa dimension.
Homotopie in homogenen komplexen Mannigfaltigkeiten.
Homotopiegruppen von Hyperflächenschnitten.
Homotopy actions, cyclic maps and their duals.
Homotopy classes that are trivial mod .
Homotopy Decompostitions of Equivariant Function Spaces.
Homotopy for small multifunctions
Homotopy groups of arc complements in or Q
Homotopy Groups of H-Spaces I
Homotopy Lie algebras and fundamental groups via deformation theory
We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as (the homotopy Lie algebra) or (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.
Homotopy nilpotent Lie groups have no torsion in homology.