Commensurating HNN extensions: nonpositive curvature and biautomaticity
Ian J Leary, Ashot Minasyan
Abstract
<p>We show that the commensurator of any quasiconvex abelian subgroup in a biauto-matic 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.</p>
Topics & Concepts
MathematicsQuasiconvex functionAbelian groupGroup (periodic table)Pure mathematicsCurvatureMathematical analysisImage (mathematics)Fundamental groupConstraint (computer-aided design)Foliation (geology)GeometryDifferential geometryNegative curvatureMean curvatureSequence (biology)Finite setGeometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyAdvanced Operator Algebra Research