Search results for "Hyperbolic group"

showing 3 items of 13 documents

Quasi-isometrically embedded subgroups of braid and diffeomorphism groups

2005

We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the $L^2$-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of $F\_n$ and $\Z^n$ for all $n>0$. As a consequence we are also able to embed a variety of Gromov hyperbolic groups quasi-isometrically in pure braid groups and in the diffeomorphism group of the disk. Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundame…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Fundamental group[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Hyperbolic groupGeneral MathematicsBraid group20F36braid groupGroup Theory (math.GR)01 natural sciencesRelatively hyperbolic group[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]right-angled Artin groupCombinatoricssymbols.namesakeMathematics - Geometric TopologyMathematics::Group Theory05C25hyperbolic group[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesBraidFOS: Mathematics0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsGeometric Topology (math.GT)Braid theoryMathematics::Geometric TopologyPlanar graphsymbols010307 mathematical physicsDiffeomorphismMathematics - Group Theory20F36; 05C25
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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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Conway irreducible hyperbolic knots with two common covers

2005

International audience; For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsQuantitative Biology::BiomoleculesCoprime integersHyperbolic groupMathematics::Number TheoryGeneral Mathematics010102 general mathematicsSkein relationHyperbolic 3-manifoldVolume conjecture01 natural sciencesRelatively hyperbolic groupMathematics::Geometric TopologyKnot theoryAlgebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences010307 mathematical physics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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