Commensurating HNN-extensions: non-positive curvature and biautomaticity

Leary, Ian, Minasyan, Ashot

2021ePrints Soton (University of Southampton)13 citations

Abstract

We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.

Topics & Concepts

Quasiconvex functionAbelian groupMathematicsPure mathematicsCurvatureGroup (periodic table)Image (mathematics)GeometryPhysicsComputer scienceArtificial intelligenceQuantum mechanicsRegular polygonConvex optimizationConvex setGeometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyAdvanced Operator Algebra Research