Geodesic
Endomorphisms, train track maps, and fully irreducible monodromies
Spencer Dowdall1 orcid ; Ilya Kapovich2 ; Christopher J. Leininger2 orcid
1Vanderbilt University, Nashville, USA
2University of Illinois at Urbana-Champaign, USA
Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1179-1200

Voir la notice de l'article provenant de la source EMS Press

DOI

Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphismof the fundamental group gives rise to an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application,we prove that the property of having fully irreducible monodromy for a splitting of a hyperbolic free-by-cyclic group depends only on the component of the BNS-invariant containing the associated homomorphism to the integers.
DOI : 10.4171/ggd/425
Classification : 20-XX, 37-XX, 57-XX
Mots-clés : Free group endomorphism, train track representative, fully irreducible automorphism, free-by-cyclic group, Bieri-Neumann-Strebel invariant

Spencer Dowdall  1   ; Ilya Kapovich  2   ; Christopher J. Leininger  2

1 Vanderbilt University, Nashville, USA
2 University of Illinois at Urbana-Champaign, USA 
Spencer Dowdall; Ilya Kapovich; Christopher J. Leininger. Endomorphisms, train track maps, and fully irreducible monodromies. Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1179-1200. doi: 10.4171/ggd/425
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     author = {Spencer Dowdall and Ilya Kapovich and Christopher J. Leininger},
     title = {Endomorphisms, train track maps, and fully irreducible monodromies},
     journal = {Groups, geometry, and dynamics},
     pages = {1179--1200},
     year = {2017},
     volume = {11},
     number = {4},
     doi = {10.4171/ggd/425},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/425/}
}
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