Relative cubulations and groups with a 2-sphere boundary
Eduard Einstein, Daniel Groves
Abstract
We introduce a new kind of action of a relatively hyperbolic group on a $\text{CAT}(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.
Topics & Concepts
MathematicsCube (algebra)Action (physics)Boundary (topology)Group (periodic table)Pure mathematicsKleinian groupCombinatoricsAlgebra over a fieldGeometryMathematical analysisPhysicsChemistryQuantum mechanicsOrganic chemistryGeometric and Algebraic TopologyTopological and Geometric Data AnalysisMathematical Dynamics and Fractals