Publication Title

Journal of Group Theory

Document Type


Department or Program


Publication Date



A group G is said to have property R ∞ R if, for every automorphism ℙ ⋯ Aut (G), the cardinality of the set of φ-twisted conjugacy classes is infinite. Many classes of groups are known to have this property. However, very few examples are known for which R ∞ R is geometric, i.e., if G has property R ∞ R, then any group quasi-isometric to G also has property R ∞ R. In this paper, we give examples of groups and conditions under which R ∞ R is preserved under commensurability. The main tool is to employ the Bieri-Neumann-Strebel invariant.

Copyright Note

This is the publisher's version of the work. This publication appears in Bates College's institutional repository by permission of the copyright owner for personal use, not for redistribution.

Required Publisher's Statement

Original version is available from the publisher at: