Corpus ID: 236154838

Random Simple-Homotopy Theory

@article{Benedetti2021RandomST,
  title={Random Simple-Homotopy Theory},
  author={Bruno Benedetti and Crystal Lai and Davide Lofano and Frank H. Lutz},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.09862}
}
We implement an algorithm RSHT (Random Simple-Homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated d-manifolds with d ≤ 6, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex… Expand

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