Quantization of conductance and the coarse cohomology of partitions

TL;DR

This paper explains how the integer quantization of Hall conductance results from the large-scale geometric properties of the sample, linking physical phenomena to coarse cohomology and higher-trace pairings.

Contribution

It introduces a geometric framework connecting Hall conductance quantization to coarse cohomology and higher-trace pairings, providing a rigorous proof of integrality.

Findings

Hall conductance quantization is derived from large-scale geometry.

The integrality of the Hall conductance is rigorously proved.

A new geometric perspective on quantum Hall effect phenomena.

Abstract

We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the Fermi projection with a coarse cohomology class coming from a partition of the geometric sample, whose integrality is proved.