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Displaying 821 – 840 of 4977

Cocycle invariants of codimension 2 embeddings of manifolds

Józef H. Przytycki, Witold Rosicki (2014)

Banach Center Publications

We consider the classical problem of a position of n-dimensional manifold Mⁿ in $ℝ^{n + 2}$ . We show that we can define the fundamental (n+1)-cycle and the shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting $M ⁿ \to ℝ^{n + 2}$ . In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in $ℝ^{n + 2}$ we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).

Codimension 2 fibrators that are closed under finite product.

Im, Young Ho, Kang, Mee Kwang, Woo, Ki Mun (1998)

International Journal of Mathematics and Mathematical Sciences

Codimension one foliations on solvable manifolds.

Shigenori Matsumoto (1993)

Commentarii mathematici Helvetici

Codimension one foliations without compact leaves.

Paul S. Schweitzer (1995)

Commentarii mathematici Helvetici

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let $ℱ$ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold $M$ . We show that if the fundamental group of each leaf of $ℱ$ is isomorphic to $Z$ , then $ℱ$ is without holonomy. We also show that if $π_{2} (M) ≅ 0$ and the fundamental group of each leaf of $ℱ$ is isomorphic to $Z^{k}$ ( $k \in Z_{\geq 0}$ ), then $ℱ$ is without holonomy.

Codimension two immersions of oriented Grassmann manifolds.

Zi-Zhou Tang (1995)

Manuscripta mathematica

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

We provide a simple characterization of codimension two submanifolds of $ℙ^{n} (ℝ)$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n \geq 6$ . If the codimension two submanifold is a nonsingular algebraic subset of $ℙ^{n} (ℝ)$ whose Zariski closure in $ℙ^{n} (ℂ)$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in $ℙ^{n} (ℝ)$ .

Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.