The Poincare conjecture for digital spaces. Properties of digital n-dimensional disks and spheres

2006/04/02 by Alexander V. Evako, Evako, Alexander V.
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computer Vision and Pattern Recognition (cs.CV) #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Topological and Geometric Data Analysis #cs.CV #cs.DM #math.AT

paper · pdf · doi:10.48550/arxiv.cs/0604004

arxiv created 2006/04/02 · openalex publication_date 2006/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the Poincare conjecture, we study properties of digital n-dimensional spheres and disks, which are digital models of their continuous counterparts. We introduce homeomorphic transformations of digital manifolds, which retain the connectedness, the dimension, the Euler characteristics and the homology groups of manifolds. We find conditions where an n-dimensional digital manifold is the n-dimensional digital sphere and discuss the link between continuous closed n-manifolds and their digital models.

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