Spectral triples for finitely presented groups, index 1

TL;DR

This paper introduces a uniform method to construct spectral triples with index 1 for a broad class of finitely presented groups using Cayley complexes and Clifford algebras.

Contribution

It provides a novel construction of spectral triples with specific index properties for finitely presented groups, extending previous approaches.

Findings

Constructs spectral triples with index 1 for many finitely presented groups

Uses Cayley complexes and Clifford algebras in the construction

Provides a uniform framework applicable to a large class of groups

Abstract

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.