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On Link Concordance and Milnor's μ Invariants
Author(s) -
Habegger Nathan,
Lin XiaoSong
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398004494
Subject(s) - mathematics , pure mathematics , string (physics) , nilpotent , concordance , surjective function , bijection , action (physics) , discrete mathematics , algebra over a field , combinatorics , medicine , physics , quantum mechanics , mathematical physics
The precise indeterminacy of Milnor's concordanceμ ¯invariants is determined. It is shown that the (nilpotent quotient) Artin representation of string links is surjective. Orr's computation of the number of linearly independentμ ¯invariants of a fixed length is recovered. A structure theorem for the set of links up to concordance is proven. We define an action of 2 l ‐component string links on l ‐component string links, which passes to concordance classes. It is shown that the set of links up to concordance is in bijection with the orbit space of the restriction of this action to the stabilizer of the identity. Via the Artin representation, the action passes to a unipotent action, defined purely algebraically and consequently algorithmically computable, on the corresponding automorphism groups. 1991 Mathematics Subject Classification 57M25.