Classification of digital n-manifolds

TL;DR

This paper introduces a method for classifying digital n-manifolds by using complexity and homotopy equivalence, including the concept of compressed n-manifolds and an algorithm applicable to any dimension.

Contribution

It proposes a new classification framework for digital n-manifolds based on homotopy and complexity, along with an algorithm for their classification across all dimensions.

Findings

Any n-manifold with p points is homotopy equivalent to a compressed n-manifold with fewer points.

The paper defines properties of compressed n-manifolds.

An algorithm for classifying digital n-manifolds of any dimension is developed.

Abstract

This paper presents the classification of digital n-manifolds based on the notion of complexity and homotopy equivalence. We introduce compressed n-manifolds and study their properties. We show that any n-manifold with p points is homotopy equivalent to a compressed n-manifold with m points, m<p. We design an algorithm for the classification of digital n-manifolds of any dimension n.