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Finitely generated infinite simple groups of homeomorphisms of the real line

  • James Hyde
  • Yash LodhaEmail author
Article
  • 82 Downloads

Abstract

We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question of Rhemtulla from 1980 concerning the existence of such groups. In fact, our construction provides a family of continuum many isomorphism types of groups with these properties.

Mathematics Subject Classification

Primary: 43A07 Secondary: 20F05 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of St. AndrewsSt. AndrewsUK
  2. 2.Institute of MathematicsEPFLLausanneSwitzerland

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