On Homotopy Types of Euclidean Rips Complexes

@article{Adamaszek2017OnHT,
  title={On Homotopy Types of Euclidean Rips Complexes},
  author={Michal Adamaszek and F. Frick and A. Vakili},
  journal={Discrete & Computational Geometry},
  year={2017},
  volume={58},
  pages={526-542}
}
  • Michal Adamaszek, F. Frick, A. Vakili
  • Published 2017
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We prove that for X in the Euclidean 3-space $$\mathbb {R}^3$$R3 the natural projection map from the Rips complex of X to its shadow in $$\mathbb {R}^3$$R3 induces a surjection on fundamental groups. This partially answers a question of Chambers, de Silva, Erickson and Ghrist who studied this projection for subsets of… CONTINUE READING

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