Search results for "20F65"

showing 5 items of 5 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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The infinite dihedral group

2022

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

FOS: Mathematics20F65 (Primary) 05C25 20E08 68Q70 13F25 (Secondary)Computer Science::Symbolic ComputationGroup Theory (math.GR)Nonlinear Sciences::Cellular Automata and Lattice GasesMathematics - Group TheoryComputer Science::Formal Languages and Automata Theory
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Sub-Finsler Horofunction Boundaries of the Heisenberg Group

2020

We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics---that is, those that arise as asymptotic cones of word metrics---on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.

Pure mathematics20f69horoboundary53C23 (Primary) 20F18 20F65 (Secondary)Boundary (topology)Group Theory (math.GR)Heisenberg group01 natural sciencesdifferentiaaligeometriasub-finsler distanceMathematics - Metric Geometryhomogeneous group0103 physical sciencesFOS: MathematicsHeisenberg groupMathematics::Metric Geometry0101 mathematicsMathematicsQA299.6-433Applied Mathematics010102 general mathematicsryhmäteoriaheisenberg groupMetric Geometry (math.MG)53c2353c17Homogeneoussub-Finsler distance010307 mathematical physicsGeometry and TopologyMathematics - Group TheoryAnalysisWord (group theory)Analysis and Geometry in Metric Spaces
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On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups.

2021

AbstractThis note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi-isometric classification with the bi-Lipschitz classification. On the other hand, we study the problem whether two quasi-isometrically equivalent Lie groups may be made isometric if equipped with suitable left-invariant Riemannian metrics. We show that this is the case for three-dimensional simply connected groups, but it is not true in general for multiply connec…

Pure mathematicsDimension (graph theory)Quasi-isometricisometric53C2301 natural sciencesdifferentiaaligeometria0103 physical sciencesSimply connected spaceMathematics::Metric Geometry0101 mathematicsIsometric20F65bi-LipschitzMathematicsTransitive relationOriginal PaperLie groupsRiemannian manifold010102 general mathematics22D05ryhmäteoriaLie groupBi-Lipschitz; Classification; Isometric; Lie groups; Quasi-isometric; Riemannian manifoldRiemannian manifoldLipschitz continuityClassificationmetriset avaruudetquasi-isometricBi-LipschitzclassificationDifferential geometrygeometria010307 mathematical physicsGeometry and TopologyMathematics::Differential GeometryCounterexampleGeometriae dedicata
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Automorphisms and abstract commensurators of 2-dimensional Artin groups

2004

In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group of each such Artin group. In the case where the defining graph has no separating edge or vertex we show that the Artin group is not abstractly commensurable to any other CLTTF Artin group. If, moreover, the defining graph satisfies a further `vertex rigidity' condition, then the abstract commensurator group of the Artin group is isomorphic to its automorphism group and generated by inner automorphisms, graph automorphisms (induced from automorphisms of the…

Vertex (graph theory)20F67CommensuratorCoxeter groupCoxeter group20F36InverseGroup Theory (math.GR)Automorphism2–dimensional Artin group20F36 20F55 20F65 20F67CombinatoricsMathematics::Group Theorytriangle freeGenerating set of a groupFOS: Mathematicscommensurator groupArtin groupGeometry and TopologyIsomorphism20F5520F65graph automorphismsMathematics - Group TheoryMathematics
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