Connection between continuous and digital n-manifolds and the Poincare conjecture
<|reference_start|>Connection between continuous and digital n-manifolds and the Poincare conjecture: We 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.<|reference_end|>
@article{evako2006connection,
    title={Connection between continuous and digital n-manifolds and the Poincare
  conjecture},
    author={Alexander Evako},
    journal={arXiv preprint arXiv:cs/0608093},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0608093},
    primaryClass={cs.DM cs.CV math.AT}
}