On Geometric Aspects of Diffuse Groups

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 \ref{appendix} settles an open question by providing an example of a group which is diffuse but not left-orderable.

2010 Mathematics Subject Classification: Primary 22E40; Secondary 06F15, 57M07, 20F65

Keywords and Phrases: orderable groups, discrete subgroups of Lie groups, hyperbolic manifolds, Bieberbach groups

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