Finite Type Link Homotopy Invariants II: Milnor's $\barμ$-invariants

Details Finite Type Link Homotopy Invariants II: Milnor's $\barμ$-invariants Finite Type Link Homotopy Invariants II: Milnor's $\barμ$-invariants

1998-12-18

arxiv.org/abs/math/9812119v1

Journal of Knot Theory and Its Ramifications, Vol. 9, No. 6 (2000) 735-758

Mathematics

Geometric Topology

23 pages, many figures

Scientific paper

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.

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