Torsion homology of arithmetic lattices and K2 of imaginary fields

TL;DR

This paper investigates bounds on torsion in the homology of arithmetic lattices and applies these results to estimate K2 groups of rings of integers in totally imaginary fields, connecting geometric and algebraic number theory.

Contribution

It provides new upper bounds for torsion in homology of arithmetic lattices and links these bounds to estimates of K2 in imaginary quadratic fields.

Findings

Established upper bounds for torsion in homology of arithmetic lattices.

Derived bounds on K2 of rings of integers in totally imaginary fields.

Connected geometric homology results with algebraic K-theory estimates.

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.