Classification of $n$-component Brunnian links up to $C_n$-move
  We 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. 
Haruko Aida Miyazawa and Akira Yasuhara