{
  "abstract": "Let $(M,ω)$ be a closed monotone integral symplectic manifold with monotonicity constant $τ>0$, and let $D\\subset M$ be a symplectic hyperplane section of degree $0<k<τ$. By Biran's decomposition theorem, $M$ is the union of a symplectic disk bundle over $D$ and the skeleton of the complement $M\\setminus D$ equipped with its Liouville structure. In this paper, we compute the relative symplectic cohomology of circle subbundles of this disk bundle over $\\mathbb{Z}$ in terms of the quantum cohomology of $D$. This relative symplectic cohomology depends on the radius of the circle bundle relative to a certain critical radius. For a broad class of pairs $(M,D)$, we prove that the relative symplectic cohomology over $\\mathbb{Z}$ does not vanish for supercritical radii. Therefore, circle bundles of supercritical radii are heavy subsets, which yields infinite dimensional quasi-flats in the Hamiltonian diffeomorphism group with respect to both the Hofer metric and the spectral metric over $\\mathbb{Z}$. We also establish that if the degree $k$ of $D$ is greater than one, the skeleton of $M\\setminus D$ is SH-full over $\\mathbb{Z}/k\\mathbb{Z}$, and hence non-displaceable in $M$ by any symplectomorphism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01334",
  "author_total": 2,
  "authors": [
    {
      "name": "Hong-kwon Jo"
    },
    {
      "name": "Jungsoo Kang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qt0zxmwqr587.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01334",
  "fulltext_url": null,
  "id": "2qt0zxmwqr587",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01334",
  "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.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7215831263",
  "pdf_url": "https://arxiv.org/pdf/2610.01334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qt0zxmwqr587.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01334"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Biran decomposition and relative symplectic cohomology",
  "title_text": "Biran decomposition and relative symplectic cohomology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/2qt0zxmwqr587",
  "venue": "arXiv",
  "versions": []
}