{
  "id": "2209.08085",
  "version": "v1",
  "published": "2022-09-16T17:51:27.000Z",
  "updated": "2022-09-16T17:51:27.000Z",
  "title": "An effective estimate on Betti numbers",
  "authors": [
    "Lei Ni"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We provide an effective estimate on the Betti numbers of the loop space of a compact manifold which admits a finite Grauert tube. It implies the polynomial estimate in \\cite{Chen} after taking the radius of the tube to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-16T17:51:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "betti numbers",
      "effective estimate",
      "finite grauert tube",
      "loop space",
      "polynomial estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}