Algebraic and Geometric Topology 5 (2005), paper no. 58, pages 1471-1479.

Skein relations for Milnor's mu-invariants

Michael Polyak

Abstract. The theory of link-homotopy, introduced by Milnor, is an important part of the knot theory, with Milnor's mu-bar-invariants being the basic set of link-homotopy invariants. Skein relations for knot and link invariants played a crucial role in the recent developments of knot theory. However, while skein relations for Alexander and Jones invariants are known for quite a while, a similar treatment of Milnor's mu-bar-invariants was missing. We fill this gap by deducing simple skein relations for link-homotopy mu-invariants of string links.

Keywords. String links, link homotopy, Milnor's mu-invariants, skein relations

AMS subject classification. Primary: 57M25. Secondary: 57M27.

E-print: arXiv:math.GT/0507602

DOI: 10.2140/agt.2005.5.1471

Submitted: 9 August 2005. Accepted: 20 September 2005. Published: 30 October 2005.

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Michael Polyak
Department of mathematics, Technion, Haifa 32000, Israel

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