Two-generator subgroups of the pure braid group

Christopher J. Leininger, Dan Margalit

Research output: Contribution to journalArticlepeer-review


We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.

Original languageEnglish (US)
Pages (from-to)107-113
Number of pages7
JournalGeometriae Dedicata
Issue number1
StatePublished - 2010
Externally publishedYes


  • Free group
  • Mapping class group
  • Pure braid group

ASJC Scopus subject areas

  • Geometry and Topology


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