Digraphs and cycle polynomials for free-by-cyclic groups
| Autor: | Algom-Kfir, Yael, Hironaka, Eriko, Rafi, Kasra |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\phi \in \mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $\phi$ determines a free-by-cyclic group $\Gamma=F_n \rtimes_\phi \mathbb Z,$ and a homomorphism $\alpha \in H^1(\Gamma; \mathbb Z)$. By work of Neumann, Bieri-Neumann-Strebel and Dowdall-Kapovich-Leininger, $\alpha$ has an open cone neighborhood $\mathcal A$ in $H^1(\Gamma;\mathbb R)$ whose integral points correspond to other fibrations of $\Gamma$ whose associated outer automorphisms are themselves representable by expanding irreducible train-track maps. In this paper, we define an analog of McMullen's Teichm\"uller polynomial that computes the dilatations of all outer automorphism in $\mathcal A$. Comment: 41 pages, 20 figures |
| Databáze: | arXiv |
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