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Digraphs and cycle
polynomials for free-by-cyclic groups
Yael Algom-Kfir, Eriko Hironaka and Kasra Rafi |
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Geometry & Topology 19 (2015) 1111–1154
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Abstract |
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Let be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism determines a free-by-cyclic group and a homomorphism . By work of Neumann, Bieri, Neumann and Strebel, and Dowdall, Kapovich and Leininger, has an open cone neighborhood in whose integral points correspond to other fibrations of 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 . |
Keywords
fibrations, free-by-cyclic groups, generalizations of the
Teichmüller polynomial
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Mathematical Subject Classification 2010
Primary: 57M20
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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
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Authors |
| Yael Algom-Kfir | |
| Mathematics Department University of Haifa Mount Carmel, Haifa 31905 Israel |
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| Eriko Hironaka | |
| Department of Mathematics Florida State University 208 Love Building 1017 Academic Way Tallahassee, FL 32301-4510 USA |
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| Kasra Rafi | |
| Department of Mathematics University of Toronto Room 6290 40 George Street Toronto ON M5S 2E4 Canada |
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