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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 $Ω Σ K (ℤ, 2 d)$ , 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...

Homomorphism between Homotopy groups induced by elements of the sobolev space L1, p (M, N).

Nobumitsu Nakauchi (1993)

Manuscripta mathematica

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.

Homotopie des espaces de concordances

Jean-Louis Loday (1977/1978)

Séminaire Bourbaki

Homotopie in homogenen komplexen Mannigfaltigkeiten.

Mathias Peternell (1984/1985)

Mathematische Zeitschrift

Homotopiegruppen von Hyperflächenschnitten.

Otto Gerstner, Ludger Kaup (1973)

Mathematische Annalen

Homotopies of small categories

Marek Golasiński (1981)

Fundamenta Mathematicae

Homotopy actions, cyclic maps and their duals.

Arkowitz, Martin, Lupton, Gregory (2005)

Homology, Homotopy and Applications

Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda, Kazuhiro Kawamura (2000)

Fundamenta Mathematicae

For the n-dimensional Hawaiian earring $ℍ_{n},$ n ≥ 2, $π_{n} (ℍ_{n}, o) ≃ ℤ^{ω}$ and $π_{i} (ℍ_{n}, o)$ 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 $H_{n} (X \lor Y) ≃ H_{n} (X) \oplus H_{n} (Y) \oplus H_{n} (C X \lor C Y)$ for n ≥ 1.

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Higher homotopy groupoids and Toda brackets.

Hindernisse in dem Produkt von Suspensionen.

Höhere Whitehead Produkte der zwei dimensionalen Sphäre

Homology and homotopy groups of the complement of certain family of fibers in a critical point problem.

Homology Equivalences and a Technique of Ganea.

Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces

Homomorphism between Homotopy groups induced by elements of the sobolev space L1, p (M, N).

Homotopie de l'espace des équivalences d'homotopie fibrées

Homotopie des espaces de concordances

Homotopie in homogenen komplexen Mannigfaltigkeiten.

Homotopiegruppen von Hyperflächenschnitten.

Homotopies of small categories

Homotopy actions, cyclic maps and their duals.

Homotopy and homology groups of the n-dimensional Hawaiian earring

Homotopy classes that are trivial mod $ℱ$ .

Homotopy Decompositions of Equivariant Function Spaces. II. Function Spaces of Equivariantly Triangulated Spaces.

Homotopy Decompostitions of Equivariant Function Spaces.

Homotopy equivalent group representations and Picard groups of the burnside ring and the character ring.

Homotopy for small multifunctions

Homotopy groups of arc complements in $S^{n}$ or Q

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