A note on twisted conjugacy and generalized Baumslag-Solitar groups

摘要

A generalized Baumslag-Solitar group is the fundamental group of a graph ofgroups all of whose vertex and edge groups are infinite cyclic. Levitt provesthat any generalized Baumslag-Solitar group has property R-infinity, that is,any automorphism has an infinite number of twisted conjugacy classes. We showthat any group quasi-isometric to a generalized Baumslag-Solitar group also hasproperty R-infinity. This extends work of the authors proving that any groupquasi-isometric to a solvable Baumslag-Solitar BS(1,n) group has propertyR-infinity, and relies on the classification of generalized Baumslag-Solitargroups given by Whyte.