English

Stable components and layers

Algebraic Topology 2020-09-09 v2 Combinatorics

Abstract

Component graphs Γ0(F)\Gamma_{0}(F) are defined for arrays of sets FF, and in particular for arrays of path components for Vietoris-Rips complexes and Lesnick complexes. The path components of Γ0(F)\Gamma_{0}(F) are the {\it stable components} of the array FF. The stable components for the system of Lesnick complexes {Ls,k(X)}\{ L_{s,k}(X) \} for a finite data set XX decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.

Keywords

Cite

@article{arxiv.1905.05788,
  title  = {Stable components and layers},
  author = {J. F. Jardine},
  journal= {arXiv preprint arXiv:1905.05788},
  year   = {2020}
}

Comments

17 pages, 1 figure

R2 v1 2026-06-23T09:06:32.419Z