3-manifolds which are orbit spaces of diffeomorphisms

Abstract : In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S^2 × S^1 or irreducible. We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco-Shalen-Johannson decomposition of these manifolds are made into product circle bundles.
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Contributor : Luisa Paoluzzi <>
Submitted on : Thursday, November 3, 2011 - 11:33:52 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM


  • HAL Id : hal-00638117, version 1


Christian Bonatti, Luisa Paoluzzi. 3-manifolds which are orbit spaces of diffeomorphisms. Topology, Elsevier, 2008, 47, pp.71-100. ⟨hal-00638117⟩



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