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  • ON LINK CONCORDANCE AND MILNOR'S μ INVARIANTS

  • NATHAN HABEGGER, XIAO-SONG LIN
  • Journal:
    Bulletin of the London Mathematical Society / Volume 30 / Issue 4 / July 1998
    Published online by Cambridge University Press:
    01 July 1998, pp. 419-428
    Print publication:
    July 1998

  • The precise indeterminacy of Milnor's concordance μ 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 independent μ 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 2l-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.