Non-abelian group structure on the Urysohn space
arXiv:1403.3277
Abstract
Following the continuing interest in the Urysohn space and, more specifically, the recent problem area of finding and comparing group structures on the Urysohn space we prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We provide several open questions and problems related to this subject.
The only change in the last version is the author's grant information. V2:Substantially different version based on the referee's comments