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Link-homotopy Invariants of Finite Type

Xiao-Song Lin
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Abstract

An explicit polynomial in the linking numbers $l_{ij}$ and Milnor's triple linking numbers $μ(rst)$ on six component links is shown to be a well-defined finite type link-homotopy invariant. This solves a problem raised by B. Mellor and D. Thurston. An extension of our construction also produces a finite type link invariant which detects the invertibility for some links.

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Xiao-Song Lin. 2000-12-12. Link-homotopy Invariants of Finite Type. https://arxiv.org/abs/math/0012095

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