Homotopy, Δ-equivalence and concordance for knots in the complement of a trivial link

Thomas Fleming, Tetsuo Shibuya, Tatsuya Tsukamoto, Akira Yasuhara

研究成果: Article

抜粋

Link-homotopy and self Δ-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Δ-equivalent) to a trivial link. We study link-homotopy and self Δ-equivalence on a certain component of a link with fixing the other components, in other words, homotopy and Δ-equivalence of knots in the complement of a certain link. We show that Milnor invariants determine whether a knot in the complement of a trivial link is null-homotopic, and give a sufficient condition for such a knot to be Δ-equivalent to the trivial knot. We also give a sufficient condition for knots in the complements of the trivial knot to be equivalent up to Δ-equivalence and concordance.

元の言語English
ページ(範囲)1215-1227
ページ数13
ジャーナルTopology and its Applications
157
発行部数7
DOI
出版物ステータスPublished - 2010 5 1

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ASJC Scopus subject areas

  • Geometry and Topology

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