6533b85bfe1ef96bd12bb556
RESEARCH PRODUCT
3-manifolds which are orbit spaces of diffeomorphisms
Christian BonattiLuisa Paoluzzisubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Seifert fibrationsClass (set theory)Pure mathematicsGradient-like diffeomorphism[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Dimension (graph theory)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Space (mathematics)01 natural sciences[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesAttractorJaco–Shalen–Johannson decomposition0101 mathematicsFinite setMathematics::Symplectic Geometry[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics010102 general mathematicsMathematical analysisMathematics::Geometric Topology3-manifoldsProduct (mathematics)010307 mathematical physicsGeometry and TopologyDiffeomorphismOrbit (control theory)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-03-01 |