An unknotting theorem for delta and sharp edge-homotopy

• Autores: Ryo Nikkuni
• Localización: Mathematische Nachrichten, ISSN 0025-584X, Vol. 280, Nº. 8, 2007, págs. 897-906
• Idioma: inglés
• DOI: 10.1002/mana.200410522
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• Resumen

  • Two spatial embeddings of a graph are said to be delta (resp. sharp) edge-homotopic if they are transformed into each other by self delta (resp. sharp) moves and ambient isotopies. We show that any two spatial embeddings of a graph are delta (resp. sharp) edge-homotopic if and only if the graph does not contain a subgraph which is homeomorphic to the theta graph or the disjoint union of two 1-spheres, or equivalently G is homeomorphic to a bouquet. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)