Approximating Novikov-Shubin numbers of virtually cyclic coverings

TL;DR

This paper introduces a method to approximate Novikov-Shubin numbers for virtually cyclic coverings of CW complexes using Diophantine approximation techniques.

Contribution

It develops a novel approximation theorem for Novikov-Shubin numbers in the context of virtually cyclic fundamental groups.

Findings

Established an approximation theorem for Novikov-Shubin numbers

Connected Novikov-Shubin numbers with Diophantine approximation methods

Provided a framework for finite approximations of spectral invariants

Abstract

We assign real numbers to finite sheeted coverings of compact CW complexes designed as finite counterparts to the Novikov-Shubin numbers. We prove an approximation theorem in the case of virtually cyclic fundamental groups employing methods from Diophantine approximation.