2016/03/09 by Syrigos, Dionysios
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1603.02846
For a group G of finite Kurosh rank and for some arbiratily free product decomposition of G, G = H1 ∗ H2 ∗ ... ∗ Hr ∗ Fq, where Fq is a finitely generated free group, we can associate some (relative) outer space O(G, \H1,..., Hr \). We define the relative boundary ∂ (G, \ H1, ..., Hr \) = ∂(G, O) corresponding to the free product decomposition, as the set of infinite reduced words (with respect to free product length). By denoting Out(G, \ H1, ..., Hr \) the subgroup of Out(G) which is consisted of the outer automorphisms which preserve the set of conjugacy classes of Hi's, we prove that for the stabiliser Stab(X) of an attractive fixed point in X ∈ ∂ (G, \ H1, ..., Hr \) of an irreducible with irreducible powers automorphism relative to O, it holds that it has a (normal) subgroup B isomorphic to subgroup of \bigoplus i=1 r Out(Hi) such that Stab(X) / B is isomorphic to ℤ. The proof relies heavily on the machinery of the attractive lamination of an IWIP automorphism relative to O.