Hyperelementary assembly for K-theory of virtually abelian groups

2005/09/13 by Frank Quinn, Quinn, Frank · 2 citations
Mathematics · #19A31 #19B28 #19DXX #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.math/0509294

openalex publication_date 2005/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group, and a reduced version is torsion. Includes general material on assembly and universal spaces.

Cited by

• Bass' NK groups and cdh-fibrant Hochschild homology
• On the K- and L-theory of hyperbolic and virtually finitely generated\n abelian groups

Related

• Controlled K-theory I: Basic theory
• Assembly Maps
• The K-theory of assemblers
• On the K-theory of groups with finite asymptotic dimension
• Relative assembly maps and the K-theory of Hecke algebras in prime characteristic