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.
ASJC Scopus subject areas
- 数学 (全般)