{
  "abstract": "In this paper, we construct a generating function quadratic at infinity for any exact Lagrangian in $\\mathbb{R}^{2n}$ R 2 n that equals $\\mathbb{R}^{n}$ R n outside a compact set. Such a Lagrangian may be viewed as a Lagrangian filling of the standard Legendrian unknot $S^{n-1}$ S n − 1 in $D^{2n}$ D 2 n . Generating functions of the type we construct are related to the space $\\mathcal{M}_{\\infty }$ M ∞ considered by Eliashberg and Gromov. We also show that $\\mathcal{M}_{\\infty }$ M ∞ is the homotopy fiber of the so-called Hatcher–Waldhausen map. This further relates the study of exact Lagrangians (and Legendrians) to algebraic K-theory of spaces. Using this and Bökstedt’s result that the Hatcher–Waldhausen map is a rational homotopy equivalence, we prove that the stable Lagrangian Gauss map (relative to the boundary) of the Lagrangian is null-homotopic.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Uppsala University, Uppsala, Sweden"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Thomas Kragh",
      "orcid": "0000-0003-2618-5712"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5sdam9m3tmfnc.bib",
  "cited_by": 5,
  "doi": "10.1007/s00222-026-01428-2",
  "fulltext_url": null,
  "id": "5sdam9m3tmfnc",
  "issns": [
    "0020-9910",
    "1432-1297"
  ],
  "landing_url": "https://doi.org/10.1007/s00222-026-01428-2",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7161568735",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-18",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/5sdam9m3tmfnc.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W7161568735",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00222-026-01428-2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Geometric and Algebraic Topology",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generating functions in $\\mathbb{R}^{2n}$ and the Hatcher–Waldhausen map",
  "title_text": "Generating functions in ℝ^2n and the Hatcher–Waldhausen map",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/5sdam9m3tmfnc",
  "venue": "Inventiones mathematicae",
  "versions": []
}