The algebraic and topological K-theory of the Hilbert Modular Group

2017/06/14 by Saldaña, Luis Jorge Sánchez, Velásquez, Mario
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1706.04691

Abstract

In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of C^*-algebras, after tensoring with ℚ, by computing the source of the assembly maps in the Farrell-Jones and the Baum-Connes conjecture respectively. We also construct a model for the classifying space of the Hilbert modular group for the family of virtually cyclic subgroups.

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