Free Actions of Finite Abelian Groups on 3-Dimensional Nilmanifolds

Choi, Dong-Soon; Shin, Joonkook

doi:10.4134/jkms.2005.42.4.795

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A3 Quotients Of the Torus And Nilmanifolds2

Example 291

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Cited by 4 publications

(3 citation statements)

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“…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%

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Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group

Hammerlindl

Potrie

2015

J Topology

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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.

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“…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

confidence: 99%