Title

Distinguishing link-homotopy classes by pre-peripheral structures

Document Type

Article

Publication Title

Journal of Knot Theory and its Ramifications

Publication Date

1-1-1998

Abstract

An open problem in link-homotopy of links in S3 is classification using peripheral invariants, analogous to that of Waldhausen for links up to ambient isotopy. An approach to such a classification was outlined by Levine, but shown not to be feasible by the author. Here, we develop an approach to finding classification counterexamples. The approach requires non-injectivity of a group homomorphism that is completely determined by minimal-weight commutator numbers (equivalent to the first non-vanishing μ̄ invariants of Milnor). For non-injectivity, the minimal-weight commutator numbers must all be non-zero, and satisfy a certain system of polynomials, which we compute for 4- and 5-component links.

Volume

7

Issue

7

First Page

925

Last Page

944

DOI

10.1142/S0218216598000498

ISSN

02182165

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