{
  "id": "2001.00176",
  "version": "v1",
  "published": "2020-01-01T09:38:49.000Z",
  "updated": "2020-01-01T09:38:49.000Z",
  "title": "Cut and paste invariants of manifolds via algebraic K-theory",
  "authors": [
    "Renee Hoekzema",
    "Mona Merling",
    "Laura Murray",
    "Carmen Rovi",
    "Julia Semikina"
  ],
  "comment": "23 pages. Comments welcome!",
  "categories": [
    "math.AT",
    "math.GT",
    "math.KT"
  ],
  "abstract": "Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic $K$-theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a spectrum that recovers the classical $\\mathrm{SK}$ (\"schneiden und kleben,\" German for \"cut and paste\") groups for manifolds on $\\pi_0$, and we construct a derived version of the Euler characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-01T09:38:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic k-theory",
      "paste invariants",
      "schneiden und kleben",
      "studying scissors congruence problems",
      "inna zakharevich"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}