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.
Notes on file formats
Michael Polyak
Department of mathematics, Technion, Haifa 32000, Israel
Email: polyak@math.technion.ac.il
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