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Displaying 161 – 180 of 242

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 $N^{n}$ .

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces $X$ the natural inclusion $e : X \to β X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

Strong shape theory [Book]

J. Dydak, J. Segal (1981)

Strong surjectivity of mappings of some 3-complexes into 3-manifolds

Claudemir Aniz (2006)

Fundamenta Mathematicae

Let K be a CW-complex of dimension 3 such that H³(K;ℤ) = 0, and M a closed manifold of dimension 3 with a base point a ∈ M. We study the problem of existence of a map f: K → M which is strongly surjective, i.e. such that MR[f,a] ≠ 0. In particular if M = S¹ × S² we show that there is no f: K → S¹ × S² which is strongly surjective. On the other hand, for M the non-orientable S¹-bundle over S² there exists a complex K and f: K → M such that MR[f,a] ≠ 0.

Strong surjectivity of mappings of some 3-complexes into $M_{Q_{8}}$

Claudemir Aniz (2008)

Open Mathematics

Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and $M_{Q_{8}}$ the orbit space of the 3-sphere $𝕊^{3}$ with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ $𝕊^{3}$ . Given a point a ∈ $M_{Q_{8}}$ , we show that there is no map f:K → $M_{Q_{8}}$ which is strongly surjective, i.e., such that MR[f,a]=min(g −1(a))|g ∈ [f] ≠ 0.

Strong surjectivity of maps from 2-complexes into the 2-sphere

Marcio Fenille, Oziride Neto (2010)

Open Mathematics

Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = $\vec{d e g}$ (f) has an integer solution, here $\vec{d e g}$ (f)is the so-called vector-degree of f

Strongly homotopically stabile points

A. Lelek (1977)

Colloquium Mathematicae

Strongly homotopy-commutative monoids revisited.

Brinkmeier, Michael (2000)

Documenta Mathematica

Structural Theorems for Topological Actions of Z...-Tori on Real, Complex and Quarternionic Projective Spaces

Wu-Yi Hsiang (1974)

Commentarii mathematici Helvetici

Structures de contact sur les fibrés principaux en cercles de dimension trois

Robert Lutz (1977)

Annales de l'institut Fourier

On construit et classifie à conjugaison équivariante près toutes les formes de contact invariantes sur un fibré principal en cercles $M_{3} \to B_{2}$ ( $M$ compact). Si $\tilde{M} = S^{3}$ , les formes obtenues induisent sur $S^{3}$ des formes de contact dans chaque classe d’homotopie de 1-formes sans zéros : on en déduit que $M$ admet une infinité de structures de contact non isomorphes.