On the Existence of Finite Type Link Homotopy Invariants

Details On the Existence of Finite Type Link Homotopy Invariants On the Existence of Finite Type Link Homotopy Invariants

2000-10-21

arxiv.org/abs/math/0010206v1

Journal of Knot Theory and its Ramifications, vol. 10, no. 7, 2001, pp. 1025-1040

Mathematics

Geometric Topology

13 pages, 5 figures

Scientific paper

We show that for links with at most 5 components, the only finite type
homotopy invariants are products of the linking numbers. In contrast, we show
that for links with at least 9 components, there must exist finite type
homotopy invariants which are not products of the linking numbers. This
corrects previous errors of the first author.

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