Invariant incompressible surfaces in reducible 3-manifolds

Christoforos Neofytidis; Shicheng Wang

doi:10.1017/etds.2017.141

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arXiv · 1701.06197

Invariant incompressible surfaces in reducible 3-manifolds

Christoforos Neofytidis·Shicheng Wang

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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 $-id$, or the mapping torus of a hyperbolic automorphism.

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Christoforos Neofytidis, Shicheng Wang. 2017-01-22. Invariant incompressible surfaces in reducible 3-manifolds. https://doi.org/10.1017/etds.2017.141

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