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Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces

Dae-Woong Lee (2005)

Czechoslovak Mathematical Journal

Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of Ω Σ K ( , 2 d ) , and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same n -type problems and giving us an information about the rational homotopy...

Homotopie de l'espace des équivalences d'homotopie fibrées

Geneviève Didierjean (1985)

Annales de l'institut Fourier

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.

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.

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