On Cₙ-moves for links
Meilhan, Jean-Baptiste · Yasuhara, Akira
Original · EN
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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