On geometric aspects of diffuse groups

Steffen Kionke, Jean Raimbault, Nathan Dunfield

Research output: Contribution to journalArticle


Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view from Bowditch's paper. In particular, we discuss fundamental groups of flat and hyperbolic manifolds. Appendix B settles an open question by providing an example of a group which is diffuse but not left-orderable.

Original languageEnglish (US)
Pages (from-to)873-915
Number of pages43
JournalDocumenta Mathematica
Issue number2016
StatePublished - Jan 1 2016


  • Bieberbach groups
  • Discrete subgroups of Lie groups
  • Hyperbolic manifolds
  • Orderable groups

ASJC Scopus subject areas

  • Mathematics(all)

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    Kionke, S., Raimbault, J., & Dunfield, N. (2016). On geometric aspects of diffuse groups. Documenta Mathematica, 21(2016), 873-915.