{
  "id": "2010.13199",
  "version": "v1",
  "published": "2020-10-25T19:19:20.000Z",
  "updated": "2020-10-25T19:19:20.000Z",
  "title": "Tracking the variety of interleavings",
  "authors": [
    "Ojaswi Acharya",
    "Stella Li",
    "David Meyer",
    "Jasmine Noory"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In topological data analysis persistence modules are used to distinguish the legitimate topological features of a finite data set from noise. Interleavings between persistence modules feature prominantly in the analysis. One can show that for $\\epsilon$ positive, the collection of $\\epsilon$-interleavings between two persistence modules $M$ and $N$ has the structure of an affine variety, Thus, the smallest value of $\\epsilon$ corresponding to a nonempty variety is the interleaving distance. With this in mind, it is natural to wonder how this variety changes with the value of $\\epsilon$, and what information about $M$ and $N$ can be seen from just the knowledge of their varieties. In this paper, we focus on the special case where $M$ and $N$ are interval modules. In this situation we classify all possible progressions of varieties, and determine what information about $M$ and $N$ is present in the progression.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-25T19:19:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N31"
    ],
    "keywords": [
      "interleaving",
      "topological data analysis persistence modules",
      "finite data set",
      "persistence modules feature",
      "legitimate topological features"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}