Disks in trivial braid diagrams

  • Dehornoy P
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Abstract

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. © 2003 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Braid diagram
  • Cayley graph
  • Disk
  • Garside monoid
  • Isotopy

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Authors

  • Patrick Dehornoy

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