LAUSR

Abstract Given a group G and an automorphism φ of G, two elements x , y ∈ G are said to be φ-conjugate if x = g y φ ( g ) − 1 for some g ∈ G . The number of equivalence classes is the Reidemeister number R ( φ ) of φ, and if R ( φ ) = ∞ for all automorphisms of G, then G is said to have the R ∞ -property. A finite simple graph Γ gives rise to the right-angled Artin group A Γ , which has as generators the vertices of Γ and as relations v w = w v if and only if v and w are joined by an edge in Γ. We conjecture that all non-abelian right-angled Artin groups have the R ∞ -property and prove this conjecture for several subclasses of right-angled Artin groups.