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Delta edge-homotopy on theta curves

Published online by Cambridge University Press:  26 April 2005

RYO NIKKUNI
RYO NIKKUNI
Affiliation:
Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku-ku, Tokyo, 169-8050, Japan. e-mail: nick@kurenai.waseda.jp
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Abstract

Two spatial embeddings of a graph are said to be delta edge-homotopic if they are transformed into each other by self delta moves and ambient isotopies. In this paper we classify theta curves up to delta edge-homotopy in terms of the third coefficient of the Conway polynomial of an associated 2-component link. In particular, we show that every boundary theta curve is delta edge-homotopically trivial, and two cobordant theta curves are delta edge-homotopic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 3 , May 2005 , pp. 401 - 420
Copyright
2005 Cambridge Philosophical Society

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