Kionke, Steffen; Dunfield, Jean Raimbault

On geometric aspects of diffuse groups. With an appendix by Nathan Dunfield.

Doc. Math., J. DMV 21, 873-915 (2016)


Summary: 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 refappendix settles an open question by providing an example of a group which is diffuse but not left-orderable.

Mathematics Subject Classification

22E40, 06F15, 57M07, 20F65


orderable groups, discrete subgroups of Lie groups, hyperbolic manifolds, Bieberbach groups