2010/11/13 by F. Rodriguez Hertz, Federico Rodriguez Hertz, J. Rodriguez Hertz +6 · 1 citation
Computer Science · Mathematics · #37D99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS #msc:37D99
paper · pdf · doi:10.48550/arxiv.1011.3165
20 pages, 4 figures
arxiv created 2010/11/13 · openalex publication_date 2010/11/13 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over π1(T) is hyperbolic. We prove that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus, (2) the mapping torus of -id, and (3) the mapping torus of hyperbolic automorphisms of the 2-torus. This has consequences for instance in the context of partially hyperbolic dynamics of 3-manifolds: if there is an invariant center-unstable foliation, then it cannot have compact leaves [19]. This has lead to the first example of a non-dynamically coherent partially hyperbolic diffeomorphism with one-dimensional center bundle [19].