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Stable cohomotopy groups of compact spaces

Sławomir Nowak (2003)

Fundamenta Mathematicae

We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups $π_{s}^{k} (X)$ . Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces. For a given Hausdorff compact space X, there exists a metric compact...

Stably spherical classes in the K-homology of a finite group.

K. Knapp (1988)

Commentarii mathematici Helvetici

Steenrod Squares in Cotor

H. Uehara, B. Al-Hashimi (1974)

Manuscripta mathematica

Strong density for higher order Sobolev spaces into compact manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen (2015)

Journal of the European Mathematical Society

Given a compact manifold $N^{n}$ , an integer $k \in ℕ_{*}$ and an exponent $1 \leq p < \infty$ , we prove that the class $C^{\infty} ({\bar{Q}}^{m}; N^{n})$ of smooth maps on the cube with values into $N^{n}$ is dense with respect to the strong topology in the Sobolev space $W^{k, p} (Q^{m}; N^{n})$ when the homotopy group $π_{⌊ k p ⌋} (N^{n})$ of order $⌊ k p ⌋$ is trivial. We also prove density of maps that are smooth except for a set of dimension $m - ⌊ k p ⌋ - 1$ , without any restriction on the homotopy group of $N^{n}$ .

Suites spectrales de Serre en homotopie

André Didierjean, André Legrand (1984)

Annales de l'institut Fourier

Beaucoup d’informations sur les groupes de cohomologie d’un espace sont obtenues à partir de la suite spectrale de Serre. Dans cet article on construit une suite spectrale de Serre dans le cas “non stable”. Cette suite spectrale “non stable” permet des calculs de groupes d’homotopie d’espaces fonctionnels.