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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 [email protected]
SHICHENG WANG
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China email [email protected]
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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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References

Bonahon, F.. Cobordism of automorphisms of surfaces. Ann. Sci. Éc. Norm. Super. 16 (1983), 237–270.10.24033/asens.1448Google Scholar
César de Sá, E. and Rourke, C.. The homotopy type of homeomorphisms of 3-manifolds. Bull. Amer. Math. Soc. (N.S.) 1(1) (1979), 251–254.10.1090/S0273-0979-1979-14574-9Google Scholar
Hempel, J.. 3-Manifolds (Annales of Mathematical Studies, 86) . Princeton University Press, Princeton, NJ and University of Tokyo Press, Tokyo, 1976.Google Scholar
McCullough, D.. Mappings of Reducible 3-Manifolds (Proceedings of the Semester in Geometric and Algebraic Topology) . Warsaw, Banach Center, 1986, pp. 61–76.Google Scholar
Rodriguez Hertz, F., Rodriguez Hertz, M. and Ures, R.. Tori with hyperbolic dynamics in 3-manifolds. J. Mod. Dyn. 5(1) (2011), 185–202.Google Scholar
Rodriguez Hertz, F., Rodriguez Hertz, M. and Ures, R.. Partial hyperbolicity and ergodicity in dimension three. J. Mod. Dyn. 2(2) (2008), 187–208.Google Scholar
Zhao, X.. On the Nielsen numbers of slide homeomorphisms on 3-manifolds. Topology Appl. 136(1–3) (2004), 169–188.Google Scholar