Search results for "Fibrations"

showing 4 items of 4 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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Affine Surfaces With a Huge Group of Automorphisms

2013

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.

Normal subgrouprational fibrationsautomorphismsGroup (mathematics)General Mathematics010102 general mathematicsAutomorphism01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsMathematics::LogicMathematics - Algebraic GeometryMathematics::Group Theory0103 physical sciencesFree groupCountable setUncountable set[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics0101 mathematicsAlgebraic number14R25 14R20 14R05 14E05affine surfacesQuotientMathematicsInternational Mathematics Research Notices
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Extension theory and the calculus of butterflies

2016

Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…

TorsorCrossed moduleContext (language use)01 natural sciencesCohomologyCohomology; Extension; Fibrations; Obstruction theory; Schreier-mac lane theorem; TorsorsExtensionMathematics::Category Theory0103 physical sciences0101 mathematicsConnection (algebraic framework)MathematicsAlgebra and Number TheoryFunctorGroup (mathematics)010102 general mathematicsTorsorsExtension (predicate logic)Obstruction theorySchreier-mac lane theoremCohomologyFibrationsAlgebraSettore MAT/02 - AlgebraSchreier–Mac Lane theoremSettore MAT/03 - Geometria010307 mathematical physicsObstruction theory
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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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