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Le genre de Heegaard de 3-variétés orientables.

Phoebe Hoidn (1996)

Revista Matemática de la Universidad Complutense de Madrid

We consider irreducible, closed, oriented, connected 3-manifolds with a nontrivial fundamental group, and link Heegaard genus to fundamental domains. We shall show that the Heegaard genus is the least positive integer h(M) for which the manifold has a fundamental domain with 2·h(M) faces.

Les invariants θ p des 3-variétés périodiques

Nafaa Chbili (2001)

Annales de l’institut Fourier

Soit r un entier > 1 . Une 3-variété M est dite r -périodique si et seulement si le groupe cyclique G = / r agit semi-librement sur M avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques θ p pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.

Local moves on knots and products of knots

Louis H. Kauffman, Eiji Ogasa (2014)

Banach Center Publications

We show a relation between products of knots, which are generalized from the theory of isolated singularities of complex hypersurfaces, and local moves on knots in all dimensions. We discuss the following problem. Let K be a 1-knot which is obtained from another 1-knot J by a single crossing change (resp. pass-move). For a given knot A, what kind of relation do the products of knots, K ⊗ A and J ⊗ A, have? We characterize these kinds of relation between K ⊗ A and J ⊗ A by using local moves on high...

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