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Operations on Metric Thickenings

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 نشر من قبل EPTCS
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Henry Adams




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Many simplicial complexes arising in practice have an associated metric space structure on the vertex set but not on the complex, e.g. the Vietoris-Rips complex in applied topology. We formalize a remedy by introducing a category of simplicial metric thickenings whose objects have a natural realization as metric spaces. The properties of this category allow us to prove that, for a large class of thickenings including Vietoris-Rips and Cech thickenings, the product of metric thickenings is homotopy equivalent to the metric thickenings of product spaces, and similarly for wedge sums.



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