{
  "id": "2103.04171",
  "version": "v1",
  "published": "2021-03-06T18:21:50.000Z",
  "updated": "2021-03-06T18:21:50.000Z",
  "title": "Knot Floer homology of some even 3-stranded pretzel knots",
  "authors": [
    "Konstantinos Varvarezos"
  ],
  "comment": "39 pages, 24 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We apply the theory of \"peculiar modules\" for the Floer homology of 4-ended tangles developed by Zibrowius (specifically, the immersed curve interpretation of the tangle invariants) to compute the Knot Floer Homology ($\\widehat{HFK}$) of 3-stranded pretzel knots of the form ${P(2a,-2b-1,\\pm(2c+1))}$ for positive integers $a,b,c$. This corrects a previous computation by Eftekhary; in particular, for the case of ${P(2a,-2b-1,2c+1)}$ where $b<c$ and $b<a-1$, it turns out the rank of $\\widehat{HFK}$ is larger than that predicted by that work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-06T18:21:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18"
    ],
    "keywords": [
      "knot floer homology",
      "pretzel knots",
      "tangle invariants",
      "peculiar modules",
      "immersed curve interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}