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Caractéristiques d'euler et groupes fondamentaux des variétés de dimension 4.

J.-C. Hausmann, Shmuel Weinberger (1985)

Commentarii mathematici Helvetici

Characterization of knot complements in the n-sphere

Vo-Thanh Liem, Gerard Venema (1995)

Fundamenta Mathematicae

Knot complements in the n-sphere are characterized. A connected open subset W of $S^{n}$ is homeomorphic with the complement of a locally flat (n-2)-sphere in $S^{n}$ , n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of $S^{1}$ in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.

Classification of simple knots by Levine pairings.

Sadayoshi Kojima (1979)

Commentarii mathematici Helvetici

Cobordism of algebraic knots.

Susan Szczepanski (1989)

Inventiones mathematicae

Cobordism of algebraic knots via Seifert forms.

Philippe Du Bois, Francoise Michel (1993)

Inventiones mathematicae

Cobordisme d'enlacements de disques

Jean-Yves Le Dimet (1988)

Mémoires de la Société Mathématique de France

Cobordisme des entrelacs

Vincent Blanlœil (1998)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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).

Currently displaying 1 – 12 of 12