Search results for "3-manifolds"

showing 6 items of 6 documents

Dehn surgeries and smooth structures on 3-dimensional transitive Anosov flows.

2020

The present thesis is about Dehn surgeries and smooth structures associated with transitive Anosov flows in dimension three. Anosov flows constitute a very important class of dynamical systems, because of its persistent chaotic behaviour, as well as for its rich interaction with the topology of the ambient space. Even if a lot is known about the dynamical and ergodic properties of these systems, there is not a clear understanding about how to classify its different orbital equivalence classes. Until now, the biggest progress has been done in dimension three, where there is a family of techniques intended for the construction of Anosov flows called surgeries.During the realization of this th…

3-ManifoldsHyperbolic DynamicsDehn surgeriesFlots d' AnosovDynamique hyperboliqueSections de BirkhoffDécompositions en livre ouvert[MATH.MATH-GN] Mathematics [math]/General Topology [math.GN]Chirurgies de DehnOpen book decompositions[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]Anosov flowsBirkhoff sections3-Variétés
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Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

Discrete mathematicsPure mathematicsMathematics::Dynamical SystemsTopological classificationTopological classificationGeometry and TopologyDiffeomorphismInvariant (mathematics)Topological conjugacyMathematics::Symplectic GeometryMorse–Smale diffeomorphismsMathematics3-manifoldsTopology
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The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

2016

We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.

MSC: Primary 57M27: Invariants of knots and 3-manifolds Secondary 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$Pure mathematicsMarkov chainGeneral Mathematics010102 general mathematicsYokonuma-Hecke algebrasGeometric Topology (math.GT)Linking numbers01 natural sciencesMathematics::Geometric TopologyMatrix (mathematics)Mathematics - Geometric TopologyMarkov tracesMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)010307 mathematical physics0101 mathematicsRepresentation Theory (math.RT)Link (knot theory)Mathematics - Representation TheoryMathematics
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Some remarks on universal covers and groups

2014

We give a quick reviw of problems concerning the topological behavior of contractible covering spaces, from the point of view of the topology at infinity.

Settore MAT/03 - GeometriaUniversal covering spaces 3-manifolds.
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On the classification of Kim and Kostrikin manifolds

2006

International audience; We completely classify the topological and geometric structures of some series of closed connected orientable 3-manifolds introduced by Kim and Kostrikin in [20, 21] as quotient spaces of certain polyhedral 3-cells by pairwise identifications of their boundary faces. Then we study further classes of closed orientable 3-manifolds arising from similar polyhedral schemata, and describe their topological properties.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]3-manifolds; group presentations; spines; orbifolds; polyhedral schemata; branched coveringsAlgebra and Number TheorySeries (mathematics)010102 general mathematicsBoundary (topology)spines0102 computer and information sciences01 natural sciencesgroup presentations3-manifoldsCombinatoricspolyhedral schemata010201 computation theory & mathematics[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Pairwise comparisonorbifoldsbranched coverings0101 mathematicsQuotient[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics
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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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