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arXiv · 1307.1371

On digital simply connected spaces and manifolds: a digital simply connected 3-manifold is the digital 3-sphere

Alexander Evako
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Abstract

In the framework of digital topology, we study structural and topological properties of digital n-dimensional manifolds. We introduce the notion of simple connectedness of a digital space and prove that if M and N are homotopy equivalent digital spaces and M is simply connected, then so is N. We show that a simply connected digital 2-manifold is the digital 2-sphere and a simply connected digital 3-manifold is the digital 3-sphere. This property can be considered as a digital form of the Poincaré conjecture for continuous three-manifolds.

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Alexander Evako. 2013-07-04. On digital simply connected spaces and manifolds: a digital simply connected 3-manifold is the digital 3-sphere. https://arxiv.org/abs/1307.1371

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