FINITE TYPE INVARIANTS AND MILNOR INVARIANTS FOR BRUNNIAN LINKS
Mathematics - Geometric Topology
57M27
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
57M25
FOS: Mathematics
57M25; 57M27
Geometric Topology (math.GT)
0101 mathematics
01 natural sciences
DOI:
10.1142/s0129167x08004820
Publication Date:
2008-06-25T11:01:25Z
AUTHORS (2)
ABSTRACT
A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, Habiro 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 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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