{
  "id": "2401.11015",
  "version": "v1",
  "published": "2024-01-19T20:27:04.000Z",
  "updated": "2024-01-19T20:27:04.000Z",
  "title": "Topological complexity of Milnor fibration",
  "authors": [
    "Taciana O. Souza",
    "Cesar A. Ipanaque Zapata"
  ],
  "comment": "19 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:2208.10672, arXiv:1910.00157",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "In this paper we discover a connection between the Milnor fibration theory and current research trends in topological robotics. The configuration space and workspace are often described as subspaces of some Euclidean spaces. The work map is a continuous map which assigns to each state of the configuration space the position of the end-effector at that state. The tasking planning problem consists in study the complexity and design of algorithms controlling the task performed by the robot manipulator. We study the tasking planning problem for the Milnor fibration of analytic function-germs in the real and complex cases. The tasking algorithms strongly depends of the Milnor fibration theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-19T20:27:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological complexity",
      "configuration space",
      "current research trends",
      "milnor fibration theory",
      "milnor fibration theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}