{
  "id": "1607.08185",
  "version": "v1",
  "published": "2016-07-27T17:15:16.000Z",
  "updated": "2016-07-27T17:15:16.000Z",
  "title": "Topological complexity of n points on a tree",
  "authors": [
    "Steven Scheirer"
  ],
  "comment": "19 pages, 9 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration space in some real-life context. Here, we consider the case where $X$ is the space of configurations of $n$ points on a tree $\\Gamma.$ We will be interested in two such configuration spaces. In the, first, denoted $C^n(\\Gamma),$ the points are distinguishable, while in the second, $UC^n(\\Gamma),$ the points are indistinguishable. We determine $TC(C^n(\\Gamma))$ and $TC(UC^n(\\Gamma))$ for any tree $\\Gamma$ (provided the configuration spaces are path-connected) and many values of $n.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-27T17:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "55R80",
      "57Q05"
    ],
    "keywords": [
      "topological complexity",
      "configuration space",
      "minimum number",
      "real-life context",
      "continuous rules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}