Tree amalgamations and quasi-isometries

Abstract

We investigate the connections between tree amalgamations and quasi-isometries. In particular, we prove that the quasi-isometry type of multi-ended accessible quasi-transitive connected locally finite graphs is determined by the quasi-isometry type of their one-ended factors in any of their terminal factorisations. Our results carry over theorems of Papsoglu and Whyte on quasi-isometries between multi-ended groups to those between multi-ended graphs. In the end, we discuss the impact of our results to a question of Woess.

14 pages

Cited by in corpus (2)

• Tree amalgamations and hyperbolic boundaries
• Homotopy and Homology at Infinity and at the Boundary