A combinatorial interpretation of homotopy groups of polyhedra
A conjecture on the unstable Adams spectral sequences for SO and U
We give a systematic account of a conjecture suggested by Mark Mahowald on the unstable Adams spectral sequences for the groups SO and U. The conjecture is related to a conjecture of Bousfield on a splitting of the E₂-term and to an algebraic spectral sequence constructed by Bousfield and Davis. We construct and realize topologically a chain complex which is conjectured to contain in its differential the structure of the unstable Adams spectral sequence for SO. A filtration of this chain complex...
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A topological version of Bertini's theorem
We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
Brown's representability theorem and branched coverings.
Commutativeness of Fundamental Groups of Topological Groups
In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].
Correction to the paper "Moduli spaces of covers and the Hurwitz monodromy group".
Counting Elemnts in Homotopy Sets.
Covering maps for locally path-connected spaces
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and Zastrow....
Das K (..., 1)-Problem für die affinen Wurzelsysteme vom Typ An, Cn.
Divisibility by 2 and 3 of certain Stirling numbers.
Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets
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.
Ein Lefschetz-Satz für Schnitte in projektivalgebraischen Mannigfaltigkeiten.
Finite subset spaces of .
Free and non-free subgroups of the fundamental group of the Hawaiian Earrings
The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
Fundamental groups of one-dimensional spaces
Let X be a metrizable one-dimensional continuum. We describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from...
Homotopie des espaces de concordances
Homotopy and homology groups of the n-dimensional Hawaiian earring
For the n-dimensional Hawaiian earring n ≥ 2, and is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then for n ≥ 1.
James Numbers.