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ON LINK CONCORDANCE AND MILNOR'S μ INVARIANTS

Published online by Cambridge University Press:  01 July 1998

NATHAN HABEGGER  and
XIAO-SONG LIN
NATHAN HABEGGER
Affiliation:
UMR 6629 du CNRS, Université de Nantes, Département de Mathématiques, 2 rue de la Houssinière, 44072 Nantes Cedex 03, France
XIAO-SONG LIN
Affiliation:
UMR 6629 du CNRS, Université de Nantes, Département de Mathématiques, 2 rue de la Houssinière, 44072 Nantes Cedex 03, France
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Abstract

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.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 4 , July 1998 , pp. 419 - 428
Copyright
© The London Mathematical Society 1998

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