{
  "id": "2109.11266",
  "version": "v1",
  "published": "2021-09-23T10:10:37.000Z",
  "updated": "2021-09-23T10:10:37.000Z",
  "title": "The analytic lattice cohomology of isolated singularities",
  "authors": [
    "Tamás Ágoston",
    "András Némethi"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2108.12429, arXiv:2108.12294",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We associate (under a minor assumption) to any analytic isolated singularity of dimension $n\\geq 2$ the `analytic lattice cohomology' ${\\mathbb H}^*_{an}=\\oplus_{q\\geq 0}{\\mathbb H}^q_{an}$. Each ${\\mathbb H}^q_{an}$ is a graded ${\\mathbb Z}[U]$--module. It is the extension to higher dimension of the `analytic lattice cohomology' defined for a normal surface singularity with a rational homology sphere link. This latest one is the analytic analogue of the `topological lattice cohomology' of the link of the normal surface singularity, which conjecturally is isomorphic to the Heegaard Floer cohomology of the link. The definition uses a good resolution $\\widetilde{X}$ of the singularity $(X,o)$. Then we prove the independence of the choice of the resolution, and we show that the Euler characteristic of ${\\mathbb H}^*_{an}$ is $h^{n-1}({\\mathcal O}_{\\widetilde{X}})$. In the case of a hypersurface weighted homogeneous singularity we relate it to the Hodge spectral numbers of the first interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T10:10:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S05",
      "32S25",
      "32S50",
      "14Bxx",
      "14J80"
    ],
    "keywords": [
      "analytic lattice cohomology",
      "normal surface singularity",
      "rational homology sphere link",
      "heegaard floer cohomology",
      "hodge spectral numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}