Linear and projective boundaries in HNN-extensions and distortion phenomena

Abstract

AbstractLinear and projective boundaries of Cayley graphs were introduced in [Glasg. Math. J. (2014), DOI 10.1017/S0017089514000512] as quasi-isometry invariant boundaries of finitely generated groups. They consist of forward orbitsWe show that for all finitely generated groups, the distance between the antipodal pointsWe also exhibit a group with elements