Search results for "Geometry"

showing 10 items of 4487 documents

On codimension two embeddings up to link-homotopy

2017

We consider knotted annuli in 4-space, called 2-string-links, which are knotted surfaces in codimension two that are naturally related, via closure operations, to both 2-links and 2-torus links. We classify 2-string-links up to link-homotopy by means of a 4-dimensional version of Milnor invariants. The key to our proof is that any 2-string link is link-homotopic to a ribbon one; this allows to use the homotopy classification obtained in the ribbon case by P. Bellingeri and the authors. Along the way, we give a Roseman-type result for immersed surfaces in 4-space. We also discuss the case of ribbon k-string links, for $k\geq 3$.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsHomotopy010102 general mathematicsClosure (topology)Geometric Topology (math.GT)CodimensionMSC: 57Q45 (primary); 57M27; 57Q35 (secondary)01 natural sciencesMathematics::Geometric TopologyMathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesRibbonKey (cryptography)FOS: Mathematics010307 mathematical physicsGeometry and Topology0101 mathematicsLink (knot theory)Mathematics
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Hyperbolic isometries versus symmetries of links

2009

We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsHyperbolic groupHyperbolic linkTotally geodesic surfaces01 natural sciencesRelatively hyperbolic group57M60Mathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Hyperbolic linksHyperbolic space010102 general mathematicsHyperbolic 3-manifoldHyperbolic manifoldGeometric Topology (math.GT)Algebra010307 mathematical physicsGeometry and TopologyIsometry groupHyperbolic Dehn surgeryHyperbolic Dehn surgeryTopology and its Applications
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A note on the Lawrence-Krammer-Bigelow representation

2002

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsLinear representation[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)52C3001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]52C35Mathematics - Geometric TopologyMathematics::Group TheoryMathematics::Algebraic Geometry[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics20F36 52C35 52C30 32S22braid groups0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]linear representations010102 general mathematicsRepresentation (systemics)FibrationSalvetti complexesGeometric Topology (math.GT)Mathematics::Geometric TopologyHyperplaneMonodromy010307 mathematical physicsGeometry and TopologyMathematics - Group Theory32S22
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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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On the classification of mapping class actions on Thurston's asymmetric metric

2011

AbstractWe study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an element is zero or positive and whether the value of this translation distance is attained or not, and we relate these four types to Thurston's classification of mapping class elements. The study is parallel to the one made by Bers in the setting of Teichmüller space equipped with Teichmüller's metric, and to the one made by Daskalopoulos and Wentworth in the setting of Te…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Teichmüller spacePure mathematicsMathematics::Dynamical SystemsGeneral MathematicsProduct metric01 natural sciencesIntrinsic metricMathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics32G15 ; 30F60 ; 57M50 ; 57N05Teichmüller spaceMathematics::Complex VariablesInjective metric space010102 general mathematicsMathematical analysisThurston's asymmetric metricGeometric Topology (math.GT)mapping class groupSurface (topology)Mathematics::Geometric TopologyMapping class groupConvex metric spaceMetric (mathematics)010307 mathematical physicsMathematics::Differential Geometry
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Approche adaptative de simplification géométrique temps réel de modèles 3D distribués pour la visualisation et l'interaction à distance

2010

National audience; Deux moyens permettent aujourd'hui d'accéder visuellement à des données 3D volumineuses à distance : le premier consiste à transférer les données entre le serveur et le poste client/utilisateur, le second consiste à générer et à transférer des " photographies" de ces données 3D qui restent alors localisées sur le serveur. Le goulot d'étranglement principal dans les deux cas est la bande passante du réseau qui ne permet pas de transférer des volumes de données importants. Bien plus, la visualisation de plusieurs centaines de giga-octets d'informations nécessite de grandes capacités de stockage (disque dur ou mémoire) et des équipements de visualisation très performants (ca…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT][ MATH.MATH-AT ] Mathematics [math]/Algebraic Topology [math.AT][MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT]persistance homologique.maillage[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]visualisation 3D[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG][MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT][ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG]persistance homologiqueSimplification 3D[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]topologie
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A predictive approach for a real-time remote visualization of large meshes

2012

Déjà sur HAL; Remote access to large meshes is the subject of studies since several years. We propose in this paper a contribution to the problem of remote mesh viewing. We work on triangular meshes. After a study of existing methods of remote viewing, we propose a visualization approach based on a client-server architecture, in which almost all operations are performed on the server. Our approach includes three main steps: a first step of partitioning the original mesh, generating several fragments of the original mesh that can be supported by the supposed smaller Transfer Control Protocol (TCP) window size of the network, a second step called pre-simplification of the mesh partitioned, ge…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]geometrytopologyComputer scienceSynthèse d'image et réalité virtuelle [Informatique]Distributed computingSewingContext (language use)02 engineering and technologySolid modeling[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]SimplificationvisualisationData visualizationtopology.[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Serverpartitioning0202 electrical engineering electronic engineering information engineeringPolygon meshVisualization[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Meshbusiness.industryProcess (computing)simplification020207 software engineering[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR][INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]VisualizationIEEEmesh[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]Mesh generation[ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG]020201 artificial intelligence & image processingbusinesssewingPartitioning
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La théorie des lignes parallèles de Johann Heinrich Lambert

2014

International audience; The memoir "Theory of parallel lines" (1766) by Johannes Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though his author conceived it as an attempt to show that this geometry does not exist. In fact, Lambert developed that theory with the hope of finding a contradiction. In doing so, he obtained several fundamental results of hyperbolic geometry. This was sixty years before the first writings of Lobachevsky and Bolyai appeared in print. This book contains the first complete translation of Lambert's memoir as well as mathematical and historical commentaries.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]géométrie sphérique01-00; 01-02; 01A50 ; 53-02 ; 53-03 ; 53A05 ; 53A35.Lambertspherical geometry[ MATH.MATH-HO ] Mathematics [math]/History and Overview [math.HO]hyperbolic geometryparallèlesgéométrie hyperbolique[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO][MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO]parallel lines.parallel lines[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale

2002

L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur Terre ou programme d'exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l'angle de gîte cinématique et le coût est l'intégrale du flux thermique. Par ailleurs il y a des contraintes sur l'état (flux thermique, accélération normale et pression dynamique). Notre étude est essentiellement géométrique et fondée sur une évaluation de l'ensemble des états accessibles en tenant compte des contraintes sur l'état. On esquisse une analyse des extrémales du Principe du …

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyControl and OptimizationAcceleration (differential geometry)02 engineering and technology01 natural sciences020901 industrial engineering & automationDimension (vector space)Applied mathematics49K1570Q050101 mathematicscontrôle optimal avec contraintes sur l'étatMathematicsMars sample return010102 general mathematicsprincipes du minimum[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]State (functional analysis)arc atmosphériqueMinimum principleComputational MathematicsHeat fluxControl and Systems Engineeringmécanique célesteDynamic pressure[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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Sensitivity analysis for time optimal orbit transfer

2001

The minimum time transfer of a satellite around the Earth is studied. In order to deal numerically with low thrusts, a new method is introduced: Based on a so-called noncontrollability function, the technique treats the ha1 time as a parameter. The properties of the method arc studied by means of an infinite dimensional sensitivity analysis. The numerical results obtained by this approach for very low thrusts are given

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyControl and OptimizationApplied Mathematics010102 general mathematicsMinimum timeMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyFunction (mathematics)Management Science and Operations ResearchTime optimal01 natural sciencesArc (geometry)020901 industrial engineering & automationControl theoryTransfer (computing)Physics::Space PhysicsOrbit (dynamics)SatelliteSensitivity (control systems)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsComputingMilieux_MISCELLANEOUSMathematics
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