Connection between continuous and digital n-manifolds and the Poincare conjecture

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dc.creatorEvako, Alexander
dc.date2006-08-24
dc.date.accessioned2026-07-07T07:20:03Z
dc.date.available2026-07-07T07:20:03Z
dc.descriptionWe introduce LCL covers of closed n-dimensional manifolds by n-dimensional disks and study their properties. We show that any LCL cover of an n-dimensional sphere can be converted to the minimal LCL cover, which consists of 2n+2 disks. We prove that an LCL collection of n-disks is a cover of a continuous n-sphere if and only if the intersection graph of this collection is a digital n-sphere. Using a link between LCL covers of closed continuous n-manifolds and digital n-manifolds, we find conditions where a continuous closed three-dimensional manifold is the three-dimensional sphere. We discuss a connection between the classification problems for closed continuous three-dimensional manifolds and digital three-manifolds.
dc.description39 pages, 26 figures
dc.identifierhttps://arxiv.org/abs/cs/0608093
dc.identifierhttp://arxiv.org/abs/cs/0608093
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114849
dc.subjectDiscrete Mathematics
dc.subjectComputer Vision and Pattern Recognition
dc.subjectAlgebraic Topology
dc.titleConnection between continuous and digital n-manifolds and the Poincare conjecture
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