Self $C_2$-equivalence of two-component links and invariants of link maps

Sergey A. Melikhov

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arXiv · 1711.03514

Self $C_2$-equivalence of two-component links and invariants of link maps

Sergey A. Melikhov

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Abstract

We use Kirk's invariant of link maps $S^2\sqcup S^2\to S^4$ and its variations due to Koschorke and Kirk-Livingston to deduce results about classical links. Namely, we give a new proof of the Nakanishi-Ohyama classification of two-component links in $S^3$ up to $\Delta$-link homotopy. We also prove its version for string links, which is due (in a slightly different form) to Fleming-Yasuhara. The proofs do not use Clasper Theory.

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BibTeX RIS

Sergey A. Melikhov. 2017-11-09. Self $C_2$-equivalence of two-component links and invariants of link maps. https://arxiv.org/abs/1711.03514

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