{
  "abstract": "We develop a unified homology theory for directed partial orders (DPOs) and lattice-ordered positive cones on fields of characteristic zero. With the underlying field and its operations fixed, we define order?carrying spaces independently by topological conditions, establish a bijection with DPO positive cones, and characterize lattice orders by intersections of minimal open neighborhoods. A unified comparison theorem identifies graded Ext for region ideals with sheaf cohomology and multiplicative Tor with the reduced singular homology of truncated regions, giving a topological interpretation of the existence and preservation of reduced decompositions. We obtain canonical cohomological obstructions to lattice ordering, prove that a coefficient module for positive multiplication is flat if and only if the multiplier has a positive inverse, and show that every strict extension of positive cones on the same field produces a nonzero first Tor obstruction. Finally, we place the concrete lattice recently constructed by Bao-Zhang within this framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06261",
  "author_total": 1,
  "authors": [
    {
      "name": "Hanzhen Bao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c22z8z4j8rpp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06261",
  "fulltext_url": null,
  "id": "6c22z8z4j8rpp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06261",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06261",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c22z8z4j8rpp.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06261",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06261"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Homology and Topology of Partially Ordered Fields",
  "title_text": "Homology and Topology of Partially Ordered Fields",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/6c22z8z4j8rpp",
  "venue": "arXiv",
  "versions": []
}