2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73698We give a classification of $n$-component links up to $C_n$-move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links.Geometric Topology57M25Classification of $n$-component Brunnian links up to $C_n$-movetext