# Homological shadows of attracting laminations

### Asaf Hadari

University of Hawaii at Manoa, Honolulu, USA

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## Abstract

Given a free group $F_n$, a fully irreducible automorphism $f \in \aut$, 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.

## Cite this article

Asaf Hadari, Homological shadows of attracting laminations. Groups Geom. Dyn. 12 (2018), no. 3, pp. 837–864

DOI 10.4171/GGD/459