{
  "annotation_id": "904bfeff-438b-464f-9a86-1ddb46759e73",
  "date_created": "2026-02-17T05:53:12.330000Z",
  "date_modified": "2026-02-17T05:53:12.330000Z",
  "file_hash": "69426a7ee2bb4b21bfa9386e66783e3ca45c20694593507fbff282d4dd8544f3",
  "private": false,
  "record": {
    "abstract": "An \\emph{affine subtorus} of the compact torus $T=(S^1)^n$ is a translated copy of a Lie subgroup. Given a finite collection $T_1,\\ldots, T_k$ of such subtori, and a prime $p$, we describe an explicit chain complex that calculates the group $H_*(T-\\bigcup_{i=1}^k T_i,\\mathbb{Z}_{(p)})$. %The complex is determined by the integral homology maps induced by the inclusions $T_J\\subset T_I$ where $I\\subset J\\subset\\{1,\\ldots, k\\}$ and $T_I$ denotes $\\bigcap_{i\\in I} T_i$. Our main tool is the binomial models for spaces constructed by T.~Ekedahl. We use these results to express the groups $H_*(T-\\bigcup_{i=1}^k T_i,\\mathbb{Z})$. We also show that the Mayer-Vietoris spectral sequence that converges to the homology of $T-\\bigcup_{i=1}^k T_i$ collapses at the second page rationally, and also integrally under some assumptions on the arrangement $T_1,\\ldots, T_k$, with all extension problems being trivial in the latter case.",
    "arxiv_id": "2601.07902",
    "authors": [
      "Alexey G. Gorinov",
      "Alexander V. Zakharov"
    ],
    "categories": [
      "math.AT",
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Binomial rings, and integral homology of complements of compact toric arrangements",
    "url": "https://arxiv.org/abs/2601.07902",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "37a0ec39-7664-467f-bc99-a63e9e879cb0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}