Displaying similar documents to “Topology Preserving Edge Contraction”

Geometric types of twisted knots

Mohamed Aït-Nouh, Daniel Matignon, Kimihiko Motegi (2006)

Annales mathématiques Blaise Pascal

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Let K be a knot in the 3 -sphere S 3 , and Δ a disk in S 3 meeting K transversely in the interior. For non-triviality we assume that | Δ ∩ K | ≥ 2 over all isotopies of K in S 3 - ∂ Δ . Let K Δ , n ( ⊂ S 3 ) be a knot obtained from K by n twistings along the disk Δ . If the original knot is unknotted in S 3 , we call K Δ , n a . We describe for which pair ( K , Δ ) and an integer n , the twisted knot K Δ , n is a torus knot, a satellite knot or a hyperbolic knot.

Two signed associahedra.

Burgiel, H., Reiner, V. (1998)

The New York Journal of Mathematics [electronic only]

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Combinatorial lemmas for polyhedrons I

Adam Idzik, Konstanty Junosza-Szaniawski (2006)

Discussiones Mathematicae Graph Theory

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We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also...

An equivalence criterion for 3-manifolds.

M. R. Casali (1997)

Revista Matemática de la Universidad Complutense de Madrid

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Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.