{
  "abstract": "There are two purposes of the present paper which are interrelated. The first goal is to construct the structure of a non-unital monoidal category $\\mathfrak{Cont}$ of contact manifolds, not necessarily coorientable, by developing the contact topology \\emph{without contact forms}. The non-unital monoidal product is the functorial contact product $\\star$, called star product, introduced in \\cite{oh:shelukhin-conjecture}. We prove that the product $\\star$ is associative and there exist a collection $α= \\{α_{X,Y,Z}\\}$ of the \\emph{associator} isomorphisms $α_{X,Y,Z}: X \\star (Y\\star Z) \\cong (X \\star Y) \\star Z$ for $X, \\, Y, \\, Z \\in \\mathfrak{Cont}$, that satisfy the pentagon axiom, i.e., that the triples $(\\mathfrak{Cont}, \\star, α)$ form a nonunital monoidal category. The second goal is to develop the calculus of Legendrian correspondences, which are by definition embedded Legendrian submanifolds of the contact product $Q \\star Q'$. Legendrian correspondences will play the role of 1-morphisms in the $2$-categorical structure to be equipped with $\\mathfrak{Cont}$ whose two morphisms are contact instanton cohomologies $HI(R_{ab},R'_{ab})$ associated to a pair of Legendrian correspondences $R_{ab}, \\, R'_{ab} \\in \\mathfrak{Leg}(Q_a,Q_b)$. With this future application in mind, we define the composition of Legendrian correspondences and prove that the composition of a generic pair is again embedded and hence canonically becomes a Legendrian correspondence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15599",
  "author_total": 2,
  "authors": [
    {
      "name": "Yong-Geun Oh"
    },
    {
      "name": "Junhyuk Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ar7vzm3r54jr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15599",
  "fulltext_url": null,
  "id": "5ar7vzm3r54jr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15599",
  "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.CT"
    ],
    [
      "arxiv",
      "math.DG"
    ],
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      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7164912783",
  "pdf_url": "https://arxiv.org/pdf/2606.15599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ar7vzm3r54jr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2606.15599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-unital monoidal category of contact manifolds and Legendrian correspondence",
  "title_text": "Non-unital monoidal category of contact manifolds and Legendrian correspondence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5ar7vzm3r54jr",
  "venue": "arXiv",
  "versions": []
}