Classification of digital n-manifolds

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.

10 pages, 8 figures, Discrete Applied Mathematics, In Press, Available online 16 September 2014. arXiv admin note: text overlap with arXiv:1307.1371