On Cn-moves for links
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, and we classify n-component link-homotopically trivial Brunnian links up to Cn+1-moves.
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