4-colored Graphs and Knot/Link Complements
| Autor: | Paola Cristofori, Vladimir Tarkaev, Evgeny Fominykh, Michele Mulazzani |
|---|---|
| Přispěvatelé: | Cristofori, Paola, Fominykh, Evgeny, Mulazzani, Michele, Tarkaev, Vladimir |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
57M25
57N10 57M15 Colored graph Applied Mathematics 010102 general mathematics colored graphs Geometric Topology (math.GT) Computer experiment 01 natural sciences Mathematics::Geometric Topology Knot/link complement 3-manifolds 010101 applied mathematics Combinatorics Mathematics - Geometric Topology Knot (unit) Mathematics (miscellaneous) knot/link complements FOS: Mathematics 0101 mathematics 3-manifolds colored graphs knot/link complements 3-manifold Mathematics |
| Popis: | A representation for compact 3-manifolds with non-empty non-spherical boundary via 4-colored graphs (i.e., 4-regular graphs endowed with a proper edge-coloration with four colors) has been recently introduced by two of the authors, and an initial classification of such manifolds has been obtained up to 8 vertices of the representing graphs. Computer experiments show that the number of graphs/manifolds grows very quickly as the number of vertices increases. As a consequence, we have focused on the case of orientable 3-manifolds with toric boundary, which contains the important case of complements of knots and links in the 3-sphere. In this paper we obtain the complete catalogation/classification of these 3-manifolds up to 12 vertices of the associated graphs, showing the diagrams of the involved knots and links. For the particular case of complements of knots, the research has been extended up to 16 vertices. 19 pages, 6 figures, 3 tables; changes in Lemma 6, Corollaries 7 and 8 |
| Databáze: | OpenAIRE |
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