- journal article metadata
European Mathematical Society Publishing House
2017-12-10 23:40:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2017
4
Endomorphisms, train track maps, and fully irreducible monodromies
Spencer
Dowdall
Vanderbilt University, Nashville, USA
Ilya
Kapovich
University of Illinois at Urbana-Champaign, USA
Christopher
Leininger
University of Illinois at Urbana-Champaign, USA
Free group endomorphism, train track representative, fully irreducible automorphism, free-by-cyclic group, Bieri-Neumann-Strebel invariant
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.
Group theory and generalizations
Dynamical systems and ergodic theory
Manifolds and cell complexes
1179
1200
10.4171/GGD/425
http://www.ems-ph.org/doi/10.4171/GGD/425
12
7
2017