The Hopf–Tsuji–Sullivan dichotomy in higher rank and applications to Anosov subgroups
Marc Burger, Or Landesberg, Minju Lee, Hee Oh
Abstract
We establish an extension of the Hopf–Tsuji–Sullivan dichotomy to any Zariski dense discrete subgroup of a semisimple real algebraic group $ G $. We then apply this dichotomy to Anosov subgroups of $ G $, which surprisingly presents a different phenomenon depending on the rank of the ambient group $ G $.
Topics & Concepts
MathematicsRank (graph theory)Pure mathematicsExtension (predicate logic)Algebraic numberCombinatoricsMathematical analysisComputer scienceProgramming languageAdvanced Algebra and GeometryAdvanced Operator Algebra ResearchGeometric and Algebraic Topology