Abstract

A C_n-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 C_n-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 C_n+1-moves.

Keywords

C_n-moves, Milnor invariants, string links, Brunnian links, claspers

Mathematical Subject Classification

Primary: 57M27, 57M25

Authors