Abstract
Given a free group F_n , a fully irreducible automorphism f \in \operatorname{Aut}(F_n) , and a generic element x \in F_n , the elements f^k(x) converge in the appropriate sense to an object called an attracting lamination of f . When the action of f on \frac{F_n}{[F_n, F_n]} has finite order, we introduce a homological version of this convergence, in which the attracting object is a convex polytope with rational vertices, together with a measure supported at a point with algebraic coordinates.
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