Vol. 238, No. 1, 2008

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ISSN: 0030-8730
On Cn-moves for links

Jean-Baptiste Meilhan and Akira Yasuhara

Vol. 238 (2008), No. 1, 119–143
Abstract

A Cn-move is a local move on links defined by Habiro and Goussarov, which can be regarded as a ‘higher order crossing change’. We use Milnor invariants with repeating indices to provide several classification results for links up to Cn-moves, under certain restrictions. Namely, we give a classification up to C4-moves of 2-component links, 3-component Brunnian links and n-component C3-trivial links. We also classify n-component link-homotopically trivial Brunnian links up to Cn+1-moves.

Keywords
Cn-moves, Milnor invariants, string links, Brunnian links, claspers
Mathematical Subject Classification 2000
Primary: 57M27, 57M25
Milestones
Received: 2 November 2007
Accepted: 7 August 2008
Published: 1 November 2008
Authors
Jean-Baptiste Meilhan
Institut for Matematiske Fag
Ny Munkegade, bygning 1530
8000 Århus C
Denmark
http://home.imf.au.dk/meilhan/index.html
Akira Yasuhara
Tokyo Gakugei University
Department of Mathematics
Koganeishi
Tokyo 184-8501
Japan
http://www.u-gakugei.ac.jp/~yasuhara/