Discrete spectral triples converging to dirac operators

TL;DR

This paper demonstrates how certain discrete spectral triples can approximate the Dirac operator of a finite-dimensional manifold, providing a way to bypass previous non-existence theorems.

Contribution

It introduces series of discrete spectral triples that converge to the canonical spectral triple of a manifold, advancing the understanding of spectral geometry.

Findings

Discrete spectral triples can approximate Dirac operators

The non-go theorem of Goekeler and Schuecker can be bypassed

Provides a new approach to spectral geometry convergence

Abstract

We exhibit some series of discrete spectral triples converging to the canonical spectral triple of a finite dimensional manifold. Thus the non-go theorem of Goekeler and Schuecker is reasonably bypassed.