@article{1ee3b878b8444ee7b4c4408e71340005,
title = "Milnor invariants, 2n-moves and v n-moves forwelded string links",
abstract = "In a previous paper, the authors proved that Milnor link-homotopy invariants modulo n classify classical string links up to 2n-move and link-homotopy. As analogues to the welded case, in terms of Milnor invariants, we give here two classifications of welded string links up to 2n-move and self-crossing virtualization, and up to V n-move and self-crossing virtualization, respectively.",
keywords = "2n-move, Arrow calculus, Milnor invariant, Self-crossing virtualization, V n-move, Welded string link",
author = "MIYAZAWA, {Haruko A.} and Kodai WADA and Akira YASUHARA",
note = "Funding Information: PROOF. It is enough to show the implication (3) ⇒ (1). If σ and σ′ are (Vn + sv)-equivalent, then µσw(I ) ≡ µσ′w(I ) (mod n) for any non-repeated sequence I by Theorem 1.4. It follows from Remark 2.2 that µσw(I ) = µσ (I ) and µσ′w(I ) = µσ′ (I ). Hence, Theorem 1.1 completes the proof. □ ACKNOWLEDGMENT. The second author was supported by Grants-in-Aid for JSPS Research Fellow (No. 17J08186 and No. 19J00006) of the Japan Society for the Promotion of Science. The third author was partially supported by a Grant-in-Aid for Scientific Research (C) (No. 17K05264) of the Japan Society for the Promotion of Science and a Waseda University Grant for Special Research Projects (No. 2018S-077). Publisher Copyright: {\textcopyright} 2021 International Academic Printing Co. Ltd.. All rights reserved.",
year = "2021",
month = jul,
doi = "10.3836/tjm/1502179315",
language = "English",
volume = "44",
pages = "49--68",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "1",
}