Skein relations for Milnor’s μ-invariants

Polyak, Michael

doi:10.2140/agt.2005.5.1471

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

Michael Polyak

Algebraic & Geometric Topology 5 (2005) 1471–1479

DOI: 10.2140/agt.2005.5.1471

arXiv: math.GT/0507602

Abstract

The theory of link-homotopy, introduced by Milnor, is an important part of the knot theory, with Milnor’s $\bar{μ}$ –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 $\bar{μ}$ –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

Volume 5, issue 4 (2005)