On the ranks of the algebraic K-Theory of hyperbolic groups

2015/11/09 by Daniel Juan-Pineda, Juan-Pineda, Daniel, Luis Jorge Sánchez Saldaña +1
Mathematics · #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) #math.GT #math.KT

paper · pdf · doi:10.48550/arxiv.1511.02767

9 pages, 1 figure

arxiv created 2015/11/09 · openalex publication_date 2015/11/09 · arxiv updated 2015/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a word hyperbolic group. We prove that the algebraic K-theory groups of \dbZ [G], K_n(\dbZ[G]), have finite rank for all n∈ \dbZ. For a few classes of groups, we give explicit formulas for the ranks of the algebraic K-theory groups of their group rings.

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