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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Digraphs and cycle polynomials for free-by-cyclic groups

Yael Algom-Kfir, Eriko Hironaka and Kasra Rafi

Geometry & Topology 19 (2015) 1111–1154
Abstract

Let ϕ Out(Fn) be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism ϕ determines a free-by-cyclic group Γ = Fn ϕ and a homomorphism α H1(Γ; ). By work of Neumann, Bieri, Neumann and Strebel, and Dowdall, Kapovich and Leininger, α has an open cone neighborhood A in H1(Γ; ) whose integral points correspond to other fibrations of Γ whose associated outer automorphisms are themselves representable by expanding irreducible train-track maps. In this paper, we define an analog of McMullen’s Teichmüller polynomial that computes the dilatations of all outer automorphisms in A.

Keywords
fibrations, free-by-cyclic groups, generalizations of the Teichmüller polynomial
Mathematical Subject Classification 2010
Primary: 57M20
References
Publication
Received: 2 February 2014
Revised: 2 February 2014
Accepted: 18 May 2014
Published: 10 April 2015
Proposed: Ian Agol
Seconded: Walter Neumann, Benson Farb
Authors
Yael Algom-Kfir
Mathematics Department
University of Haifa
Mount Carmel, Haifa 31905
Israel
Eriko Hironaka
Department of Mathematics
Florida State University
208 Love Building
1017 Academic Way
Tallahassee, FL 32301-4510
USA
Kasra Rafi
Department of Mathematics
University of Toronto
Room 6290
40 George Street
Toronto ON M5S 2E4
Canada