Around Poincare duality, in discrete spaces

TL;DR

This paper explores K-theoretic Poincare Duality in finite algebras, aiming to connect discrete noncommutative geometries with continuum Dirac operators, advancing the understanding of noncommutative manifolds.

Contribution

It provides a framework linking discrete noncommutative spaces with continuum Dirac operators through Poincare duality in K-theory.

Findings

Established a connection between discrete noncommutative algebras and continuum Dirac operators.

Developed a theoretical landscape for Poincare duality in finite noncommutative geometries.

Paved the way for future research in deriving continuum geometries from discrete models.

Abstract

We walk out the landscape of K-theoretic Poincare Duality for finite algebras. It paves the way to get continuum Dirac operators from discrete noncommutative manifolds.