{
  "abstract": "In a previous work we conjectured that the multi-invariants of the ground state of a gapped $(d-1)+1$-dimensional system, labeled by bipartite $(d+1)$-edge-colored graphs encoding closed oriented $d$-manifolds $M$, compute the partition functions $Z(M)$ of the low energy topological quantum field theory (TQFT), up to non-universal factors determined by the local structure of the triangulation. In this paper we determine which combinations of partition functions can be isolated from the non-universal factors. The answer is governed by oriented bordism. If $M$ is null-bordant, $Z(M)$ is obtained from an explicit, state-independent finite family of multi-invariants, up to a power of $Z(S^d)$ which is fixed to be $Z(S^d)^{χ(M)/2}$ for even $d$ and can be removed for odd $d$. Conversely, the obstruction is measured by a quotient of the group of \"residues\" of colored graphs which receives a surjective map from the oriented bordism group, with kernel precisely the torsion subgroup as far as smooth manifolds are concerned. In $d=4$ the obstruction is the signature: $Z(M)/Z(S^4)^{χ(M)/2}$ can be extracted if and only if $σ(M)=0$. This is due to the fact that the first Pontryagin class $p_1$ has a local expression and thus $e^{iθσ(M)}=e^{\\frac{i}{3}θ\\int_M p_1}$ cannot be separated from the non-universal factors. Torsion invariants, in contrast, are not obstructed: for the ground state of the $4+1$-dimensional invertible phase with partition function $(-1)^{\\int w_2w_3}$ we compute the multi-invariants exactly, and two graphs with identical local data, encoding the Dold manifold and $\\mathbb{CP}^2\\times S^1$, give opposite signs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07000",
  "author_total": 3,
  "authors": [
    {
      "name": "Michele Del Zotto"
    },
    {
      "name": "Abhijit Gadde"
    },
    {
      "name": "Pavel Putrov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38xs9eh42t26t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07000",
  "fulltext_url": null,
  "id": "38xs9eh42t26t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07000",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38xs9eh42t26t.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multipartite Entanglement, TQFT Partition Functions and PL Bordism",
  "title_text": "Multipartite Entanglement, TQFT Partition Functions and PL Bordism",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/38xs9eh42t26t",
  "venue": "arXiv",
  "versions": []
}