Search results for " 20F65"

showing 2 items of 2 documents

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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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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