Search results for "Seifert fibrations"

showing 2 items of 2 documents

On hyperbolic type involutions

2001

We give a bound on the number of hyperbolic knots which are double covered by a fixed (non hyperbolic) manifold in terms of the number of tori and of the invariants of the Seifert fibred pieces of its Jaco-Shalen-Johannson decomposition. We also investigate the problem of finding the non hyperbolic knots with the same double cover of a hyperbolic one and give several examples to illustrate the results.

Bonahon-Siebenmann decomposition[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Seifert fibrationsMathematics::Dynamical Systemscyclic branched coversMathematics::Geometric Topology57M5057M6057M12[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]57M25orbifoldshyperbolic knots[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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3-manifolds which are orbit spaces of diffeomorphisms

2008

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.

[ 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)
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