Algebraic & Geometric Topology

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

Michael Polyak

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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.

Article information

Algebr. Geom. Topol., Volume 5, Number 4 (2005), 1471-1479.

Received: 9 August 2005
Accepted: 20 September 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

string links link homotopy Milnor's $\mu$–invariants skein relations


Polyak, Michael. Skein relations for Milnor's $\mu$-invariants. Algebr. Geom. Topol. 5 (2005), no. 4, 1471--1479. doi:10.2140/agt.2005.5.1471.

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