Clusters, currents, and whitehead’s algorithm

Ilya Kapovich

Research output: Contribution to journalArticlepeer-review


Using geodesic currents, we provide a theoretical justification for some of the experimental results obtained by Haralick, Miasnikov, and Myasnikov via pattern-recognition methods regarding the behavior of Whitehead’s algorithm on nonminimal inputs. In particular, we prove that the images of “random” elements of a free group F under the automorphisms of F form “clusters” that share similar normalized Whitehead graphs and similar behavior with respect to Whitehead’s algorithm.

Original languageEnglish (US)
Pages (from-to)67-76
Number of pages10
JournalExperimental Mathematics
Issue number1
StatePublished - 2007
Externally publishedYes


  • Free groups
  • Genericity
  • Geodesic currents
  • Whitehead’s algorithm

ASJC Scopus subject areas

  • Mathematics(all)


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