We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite type invariants within linking classes.
Finite Type Link Homotopy Invariants II: Milnor's invariantsJournal of Knot Theory and Its Ramifications
Document TypeArticle - pre-print
Citation InformationMellor, B., 2000: Finite Type Link Homotopy Invariants II: Milnor's invariants. J. Knot Theory Ramif., 9.6, 735-758, arXiv:math/9812119.