Braids in trivial braid diagrams

We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin--Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.

• Publication year

  2003

• Venue

  arXiv: Geometric Topology

• Publication date

  2003-11-19

• Fields of study

  Mathematics

• Identifiers
  arXiv math/0311326
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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