“…Proposition A. 10. Suppose that f M is a partially hyperbolic diffeomorphism on a 3-manifold M with virtually abelian fundamental group and that there is no 2-torus tangent to…”
Section: A3 Quotients Of the Torus And Nilmanifoldsmentioning
confidence: 99%
“…As in the proofs of Propositions A.7 and A.8, we may assume that the elements of Γ are affine maps. (See [10,19].) As explained in [16,Section 2], to every homeomorphism of N k is associated an automorphism of the Lie algebra h, and this automorphism can be written…”
Section: A3 Quotients Of the Torus And Nilmanifoldsmentioning
Abstract. A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures by Rodriguez Hertz-Rodriguez Hertz-Ures ([RHRHU 2 ]) and Pujals ([BoW]) in the specific case of solvable fundamental group.
“…Proposition A. 10. Suppose that f M is a partially hyperbolic diffeomorphism on a 3-manifold M with virtually abelian fundamental group and that there is no 2-torus tangent to…”
Section: A3 Quotients Of the Torus And Nilmanifoldsmentioning
confidence: 99%
“…As in the proofs of Propositions A.7 and A.8, we may assume that the elements of Γ are affine maps. (See [10,19].) As explained in [16,Section 2], to every homeomorphism of N k is associated an automorphism of the Lie algebra h, and this automorphism can be written…”
Section: A3 Quotients Of the Torus And Nilmanifoldsmentioning
Abstract. A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures by Rodriguez Hertz-Rodriguez Hertz-Ures ([RHRHU 2 ]) and Pujals ([BoW]) in the specific case of solvable fundamental group.
The purpose of this paper is to generalize Yalçin's result [Trans. Amer. Math. Soc. 352, 2689-2700 (2000)] from tori to solvmanifolds. As a result, we prove that if (Zp) r acts freely on a solvmanifold M of dimension n, then r ≤ n.
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