Title

Finite type link homotopy invariants of k-trivial links

Document Type

Article

Publication Title

Journal of Knot Theory and its Ramifications

Publication Date

5-1-2003

Abstract

In a recent paper, Xiao-Song Lin gave an example of a finite type invariant of links up to link homotopy that is not simply a polynomial in the pairwise linking numbers. Here we present a reformulation of the problem of finding such polynomials using the primary geometric obstruction homomorphism, previously used to study realizability of link group automorphisms by link homotopies. Using this reformulation, we generalize Lin's results to k-trivial links (links that become homotopically trivial when any k components are deleted). Our approach also gives a method for finding torsion finite type link homotopy invariants within "linking classes," generalizing an idea explored earlier in [1] and [10], and yielding torsion invariants within linking classes that are different from Milnor's invariants in their original indeterminacy.

Volume

12

Issue

3

First Page

375

Last Page

393

DOI

10.1142/S0218216503002524

ISSN

02182165

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