{
  "abstract": "We give invariants of pairs $(M,Γ)$ consisting of a closed connected oriented three-manifold and an oriented framed ribbon graph embedded in $M$ colored by a the Drinfeld center of a unimodular chromatic category $\\mathcal C$. This invariant generalizes the chromatic spherical and renormalized Reshetikhin-Turaev invariants of three-manifolds. We use Heegaard-Graph diagrams which represent the pair $(M,Γ)$ and use the data of a unimodular chromatic category and objects of the Drinfeld center to construct the invariant. We define a ribbon graph associated to embedded framed links to obtain an invariant of pairs $(M,L)$. We show that if $L$ is the empty link, then the invariant recovers the chromatic spherical invariant, and if $M$ is the three-sphere, then the invariant recovers the renormalized Reshetikhin-Turaev invariant from the Drinfeld center. The relationship is proven by recovering a chromatic structure for the center induced by that from $\\mathcal C$. The main theorem of the paper demonstrates that if the graph is a link $L$ colored by a generator in the Drinfeld center, then we recover the chromatic spherical invariant of the surgery manifold $M(L)$, contributing to a proof of the relationship between the chromatic spherical and renormalized Reshetikhin-Turaev invariants for unimodular chromatic categories, generalizing a recent result for unimodular Hopf algebras by Reina. To this end, we give a Heegaard diagram for $M(L)$ coming from the Heegaard-Link diagram representing the pair $(M,L)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06708",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicolas Bridges"
    },
    {
      "name": "Shawn Cui"
    },
    {
      "name": "Nathan Geer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8s4hjszra6sjb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06708",
  "fulltext_url": null,
  "id": "8s4hjszra6sjb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06708",
  "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.GT"
    ],
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8s4hjszra6sjb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers",
  "title_text": "Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/8s4hjszra6sjb",
  "venue": "arXiv",
  "versions": []
}