English

Polyhedral expansions of compacta associated to finite approximations

Geometric Topology 2021-10-25 v1 Algebraic Topology

Abstract

This paper introduces some inverse sequences of different polyhedra all based on finite approximations of a compact metric space so they can be used to capture the shape type of the original space. It is shown that they are HPol-expansions, proving the so-called General Principle. We use these sequences to compute explicitly some inverse persistent homology groups of a space and measure its errors in the approximation process.

Keywords

Cite

@article{arxiv.2110.11928,
  title  = {Polyhedral expansions of compacta associated to finite approximations},
  author = {Diego Mondéjar},
  journal= {arXiv preprint arXiv:2110.11928},
  year   = {2021}
}