Two-generator subgroups of the pure braid group

Christopher J. Leininger, Dan Margalit

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume147
Issue number1
DOIs
StatePublished - 2010

Keywords

  • Free group
  • Mapping class group
  • Pure braid group

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint

Dive into the research topics of 'Two-generator subgroups of the pure braid group'. Together they form a unique fingerprint.

Cite this