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Invariant incompressible surfaces in reducible 3-manifolds

Published online by Cambridge University Press:  24 January 2018

CHRISTOFOROS NEOFYTIDIS  and
SHICHENG WANG
CHRISTOFOROS NEOFYTIDIS
Affiliation:
Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland email Christoforos.Neofytidis@unige.ch
SHICHENG WANG
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China email wangsc@math.pku.edu.cn
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Abstract

We study the effect of the mapping class group of a reducible 3-manifold $M$ on each incompressible surface that is invariant under a self-homeomorphism of $M$. As an application of this study we answer a question of F. Rodriguez Hertz, M. Rodriguez Hertz, and R. Ures: a reducible 3-manifold admits an Anosov torus if and only if one of its prime summands is either the 3-torus, the mapping torus of $-\text{id}$, or the mapping torus of a hyperbolic automorphism.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 3136 - 3143
Copyright
© Cambridge University Press, 2018 

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