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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 μ̄–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 μ̄–invariants was missing. We fill this gap by deducing simple skein relations for link-homotopy μ–invariants of string links.

Keywords
string links, link homotopy, Milnor's $\mu$–invariants, skein relations
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
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Publication
Received: 9 August 2005
Accepted: 20 September 2005
Published: 30 October 2005
Authors
Michael Polyak
Department of mathematics
Technion
Haifa 32000
Israel