Pith. sign in

REVIEW 4 cited by

Non-semisimple WRT at the boundary of Crane-Yetter

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.20905 v1 pith:VBABLVC4 submitted 2025-03-26 math.QA math.CTmath.GT

Benjamin Haïoun This is my paper
classification math.QAmath.CTmath.GT
keywords non-semisimpleboundarytqftarxivconditioncrane-yettercaseprove
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We prove the slogan, promoted by Walker and Freed-Teleman twenty years ago, that "The Witten-Reshetikhin-Turaev 3-TQFT is a boundary condition for the Crane-Yetter 4-TQFT" and generalize it to the non-semisimple case following ideas of Jordan, Reutter and Walker. To achieve this, we prove that the Crane-Yetter 4-TQFT and its non-semisimple version arXiv:2306.03225 are once-extended TQFTs, using the main result of arXiv:2412.14649. We define a boundary condition, partially defined in the non-semisimple case, for this 4D theory. When the ribbon category used is modular, possibly non-semisimple, we check that the composition of this boundary condition with the values of the 4-TQFT on bounding manifolds reconstructs the Witten-Reshetikhin-Turaev 3-TQFTs and their non-semisimple versions arXiv:1912.02063, in a sense that we make precise.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fully local Reshetikhin-Turaev theories

    math.QA 2026-01 conditional novelty 8.0 of 10

    Reshetikhin–Turaev theories are fully localized by enlarging the 3-category of fusion categories with a μ6 (bosonic) and μ24 (fermionic) central extension of the Witt group.

  2. The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory

    math.QA 2025-07 conditional novelty 8.0 of 10

    For any non-semisimple modular category, special symmetric Frobenius algebras now give all consistent open-closed correlators, with a holographic description and a Batalin-Vilkovisky structure on local operators.

  3. Cochain valued TQFTs from nonsemisimple modular tensor categories

    math.QA 2025-07 conditional novelty 7.0 of 10

    The authors construct a symmetric monoidal functor from admissible ribbon bordisms labeled by cochains over a modular tensor category to linear cochain complexes, extending the DGGPR TQFT and preserving homotopy equivalences.

  4. Is Crane--Yetter fully extended?

    math-ph 2025-06 conditional novelty 6.0 of 10

    Fully extended invertible 4D TQFTs valued in braided fusion categories form a Z/6-extension of the Witt group, so Crane-Yetter has six inequivalent point-refinements for fixed modular data.

Pith tools