On geometric aspects of diffuse groups. With an appendix by Nathan Dunfield. (Q321885)

Summary: \textit{B. H. Bowditch} [J. Lond. Math. Soc., II. Ser. 62, No. 3, 813--826 (2000; Zbl 1033.20040)] 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.