2024/07/02 by Bruce, Chris, Kubota, Yosuke, Takeishi, Takuya
#11R04 #22A22 #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Operator Algebras (math.OA) #Primary 46L80 #Secondary 37A55
paper · doi:10.48550/arxiv.2407.01952
We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homology of the topological full groups associated with rings of algebraic integers, and we use our groupoid homology calculation to compute the K-theory for ring C*-algebras of rings of algebraic integers, recovering the results of Cuntz and Li and of Li and Lück without using Cuntz--Li duality. Moreover, we compute the K-theory for C*-algebras attached to integral dynamics, resolving the conjecture by Barlak, Omland, and Stammeier in full generality.