Local moves for links with common sublinks

Jean Baptiste Meilhan, Eri Seida, Akira Yasuhara

Research output: Contribution to journalArticle

Abstract

A Ck-move is a local move that involves k+1 strands of a link. A Ck-move is called a Ckd-move if these k+1 strands belong to mutually distinct components of a link. Since a Ckd-move preserves all k-component sublinks of a link, we consider the converse implication: are two links with common k-component sublinks related by a sequence of Ckd-moves? We show that the answer is yes under certain assumptions, and provide explicit counter-examples for more general situations. In particular, we consider (n, k)-Brunnian links, i.e. n-component links whose k-component sublinks are all trivial. We show that such links can be deformed into a trivial link by Ckd-moves, thus generalizing a result of Habiro and Miyazawa-Yasuhara, and deduce some results on finite type invariants of (n, k)-Brunnian links.

Original languageEnglish
Pages (from-to)836-843
Number of pages8
JournalTopology and its Applications
Volume160
Issue number6
DOIs
Publication statusPublished - 2013 Apr 1

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Keywords

  • Brunnian link
  • C-moves
  • Claspers

ASJC Scopus subject areas

  • Geometry and Topology

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