Torsion homology of arithmetic lattices and K₂ K 2 of imaginary fields

2013/03/31 by Vincent Emery · 5 citations
Computer Science · Mathematics · #Algebraic number field #Arithmetic #Commutative Algebra and Its Applications #Discrete mathematics #Homology (biology) #Mathematical Dynamics and Fractals #Mathematics #Pure mathematics #Ring of integers #The Imaginary #Topological and Geometric Data Analysis #Torsion (gastropod) #math.GT #math.KT #math.NT

paper · pdf · doi:10.1007/s00209-014-1298-2

published in Mathematische Zeitschrift 277(3-4), 1155-1164 (Springer Science+Business Media) · Version 2 is a major update. Result for S-integers added. This allows to show case d=2 (imaginary quadratic fields) and d=4 in Theorem 1.3, previously excluded. 12 pages (previously 6)

arxiv created 2013/09/10 · openalex publication_date 2014/03/25 · arxiv updated 2015/04/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.

Citations

• Algebraic K-Theory of Rings of Integers in Local and Global Fields
• A torsion Jacquet--Langlands correspondence

Cited by

• Sparse Random Covers and Growth of Torsion in First Homology