Finite type invariants and Milnor invariants for Brunnian links

Details Finite type invariants and Milnor invariants for Brunnian links Finite type invariants and Milnor invariants for Brunnian links

2005-10-25

arxiv.org/abs/math/0510534v4

Int. J. Math.19, No. 6 (2008), 747-766

Mathematics

Geometric Topology

15 pages, 13 figures. A remark added, references updated

Scientific paper

A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any Goussarov-Vassiliev finite type invariant of (n+1)-component links of degree<2n is trivial. The purpose of this paper is to study the first nontrivial case. We will show that the restriction of an invariant of degree 2n to (n+1)-component Brunnian links can be expressed as a quadratic form on the Milnor link-homotopy invariants of length n+1.

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