#### Volume 5, issue 4 (2005)

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Skein relations for Milnor's $\mu$-invariants

### Michael Polyak

Algebraic & Geometric Topology 5 (2005) 1471–1479
 arXiv: math.GT/0507602
##### Abstract

The theory of link-homotopy, introduced by Milnor, is an important part of the knot theory, with Milnor’s $\stackrel{̄}{\mu }$–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 $\stackrel{̄}{\mu }$–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
Primary: 57M25
Secondary: 57M27