Page 1 Next

Displaying 1 – 20 of 49

Showing per page

A conjecture on the unstable Adams spectral sequences for SO and U

Kathryn Lesh (2002)

Fundamenta Mathematicae

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

Katsuya Eda, Umed H. Karimov, Dušan Repovš (2007)

Fundamenta Mathematicae

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

Artur Piękosz (1995)

Annales Polonici Mathematici

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 π V : V Y 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).

Covering maps for locally path-connected spaces

N. Brodskiy, J. Dydak, B. Labuz, A. Mitra (2012)

Fundamenta Mathematicae

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....

Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets

Yves Félix, Jean-Claude Thomas (1989)

Annales de l'institut Fourier

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.

Free and non-free subgroups of the fundamental group of the Hawaiian Earrings

Andreas Zastrow (2003)

Open Mathematics

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

Gerhard Dorfer, Jörg M. Thuswaldner, Reinhard Winkler (2013)

Fundamenta Mathematicae

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...

Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda, Kazuhiro Kawamura (2000)

Fundamenta Mathematicae

For the n-dimensional Hawaiian earring n , n ≥ 2, π n ( n , o ) ω and π i ( n , o ) 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 H n ( X Y ) H n ( X ) H n ( Y ) H n ( C X C Y ) for n ≥ 1.

Currently displaying 1 – 20 of 49

Page 1 Next