On the recognition of braids

Alexander A. Gaifullin, Vassily O. Manturov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A simple complete combinatorial invariant for elements of the braid group is found. It admits some generalizations, e.g. a complete invariant of spherical braids and a complete invariant of cylindrical braids. Values of the invariants are well recognizable, i.e.: they provide the complete algorithmic classification of elements in the named braid groups.

Original languageEnglish
Pages (from-to)1193-1209
Number of pages17
JournalJournal of Knot Theory and its Ramifications
Issue number8
Publication statusPublished - Dec 2002
Externally publishedYes


  • Braid
  • Braid Group
  • Cylindrical Braid
  • Spherical Braid
  • Word Problem


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