{
  "abstract": "We study the negative gradient flow of analytic maps $f:X\\to\\R$ defined on compact analytic Riemannian manifolds without imposing any nondegeneracy or transversality assumptions. We construct tight isolating blocks around the connected components of the critical set $\\Crit(f)$ and record only bounded-time contacts made after an orbit exits one block and before it makes landfall within the interior of another. These contacts assemble into a strict topological category $\\cL$ -- called the landfall category -- whose classifying space $B\\cL$ is shown to be simple homotopy equivalent to $X$ naturally over all down-sets of the flow partial order. The filtered homotopy type is independent of the isolating blocks. Passing to a finite subanalytic triangulation yields a flow-induced acyclic partial matching, and hence, an explicit finite chain complex generated by the non-exit simplices of the blocks which computes the homology of $X$. The finite model also computes the Morse--Conley spectral sequence over arbitrary coefficients; over a field, homological perturbation further produces a connection matrix whose entries are finite sums over descending contact itineraries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30993",
  "author_total": 2,
  "authors": [
    {
      "name": "Frances Kirwan"
    },
    {
      "name": "Vidit Nanda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3z430dydmvm9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30993",
  "fulltext_url": null,
  "id": "b3z430dydmvm9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30993",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223327185",
  "pdf_url": "https://arxiv.org/pdf/2610.30993",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3z430dydmvm9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30993",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30993"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Landfall Geometry",
  "title_text": "Landfall Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/b3z430dydmvm9",
  "venue": "arXiv",
  "versions": []
}