Search results for "right-angled Artin group"

showing 4 items of 4 documents

Automorphisms of 2–dimensional right-angled Artin groups

2007

We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. 20F36; 20F65, 20F28

20F36outer spaceCohomological dimensionComputer Science::Digital LibrariesQuantitative Biology::Other01 natural sciencesContractible spaceUpper and lower boundsCombinatorics0103 physical sciences20F650101 mathematicsAlgebraic numberMathematics20F28Quantitative Biology::Biomolecules010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsOuter automorphism groupAutomorphismGraphArtin groupright-angled Artin groups010307 mathematical physicsGeometry and Topologyouter automorphismsGeometry & Topology
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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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Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups

2003

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) never embeds in a right-angled Artin group.

graph groupBraid group20F36Group Theory (math.GR)Graphright-angled Artin groupCombinatorics20F36 05C25 05C25symbols.namesakeMathematics::Group Theory05C25Euler characteristicFOS: MathematicssymbolsBraidEmbeddingArtin groupGeometry and Topologygraph braid groupMathematics - Group Theoryconfiguration spacecubed complexMathematics
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Automorphisms of right-angled Artin groups

2012

The purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph $\Gamma$, the right-angled Artin group $G_\Gamma$ associated to $\Gamma$ is the group defined by the presentation whose generators are the vertices of $\Gamma$, and whose relators are commutators of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automorphisms. In a second chapter, we prove that every subnormal subgroup of $p$-power index in a right-angled Artin group is conjugacy $p$-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in th…

propriétés de séparabilitétopologie pro-ppropriétés résiduellespresentation of a group.automorphism groupgroupe d'automorphismesTorelli grouppro-p topologygroupe de TorelliRight-angled Artin groupprésentation d'un groupe.residual propertiesseparability propertiesGroupe d'Artin à angles droits[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
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