Search results for " 57M"

showing 4 items of 24 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
researchProduct

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
researchProduct

From braid groups to mapping class groups

2005

This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT][ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]20F3620F36; 57M99Geometric Topology (math.GT)Group Theory (math.GR)[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Mathematics - Geometric Topology57M99[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsMathematics - Group Theory[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR][MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Proceedings of Symposia in Pure Mathematics
researchProduct

On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

2002

Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.

nonpositive curvatureGroup (mathematics)20F6720F67 57M20Geometric Topology (math.GT)Group Theory (math.GR)Cohomological dimensionEuclidean distanceCombinatoricsKernel (algebra)Mathematics::Group TheoryMathematics - Geometric Topologydimension57M20Dimension (vector space)FOS: MathematicsArtin groupflag complexGeometry and TopologyArtin groupMathematics - Group TheoryZero-dimensional spaceMathematicsFlag (geometry)
researchProduct