2025/12/26 by Sahana Balasubramanya, Balasubramanya, Sahana, Talia Fernós +1
Computer Science · Mathematics · #20F65 #20F67 #Advanced Operator Algebra Research #Cellular Automata and Applications #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2512.21936
openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of δ-hyperbolic spaces with general type factors and associated subdirect products. This work is inspired by the classical theory of S-arithmetic lattices and the flourishing theory of acylindrically hyperbolic groups. In this paper - the first of three - we develop various fundamental results, explore elementary subgroups in higher rank, and exhibit a free vs abelian Tits Alternative. Along the way we give representation-theoretic proofs of various results about acylindricity -- some methods are new even in the rank-one setting. The vastness of this class of groups is exhibited by recognizing that it contains S-arithmetic lattices with rank-one factors, acylindrically hyperbolic groups, colorable HHGs, groups with property (QT), and enjoys robust stability properties.