{
  "id": "1701.03483",
  "version": "v1",
  "published": "2017-01-12T19:49:00.000Z",
  "updated": "2017-01-12T19:49:00.000Z",
  "title": "Invitation to Alexandrov geometry: CAT[0] spaces",
  "authors": [
    "Stephanie Alexander",
    "Vitali Kapovitch",
    "Anton Petrunin"
  ],
  "comment": "96 pages, 31 figures",
  "categories": [
    "math.DG",
    "math.AT",
    "math.MG"
  ],
  "abstract": "The idea is to demonstrate the beauty and power of Alexandrov geometry by reaching interesting applications with a minimum of preparation. The applications include 1. Estimates on the number of collisions in billiards. 2. Construction of exotic aspherical manifolds. 3. The geometry of two-convex sets in Euclidean space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-12T19:49:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53-01",
      "53C23",
      "53C45"
    ],
    "keywords": [
      "alexandrov geometry",
      "invitation",
      "exotic aspherical manifolds",
      "two-convex sets",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 96,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}