Pith. sign in

REVIEW 4 cited by

The cyclic Deligne conjecture and Calabi-Yau structures

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 2305.10323 v1 pith:W4KCWFIV submitted 2023-05-17 math.AT math.AG

Christopher Brav , Nick Rozenblyum This is my paper · ORCID
classification math.ATmath.AG
keywords linearalgebracategorystructurecalabi-yauconjecturedelignecochains
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The Deligne conjecture (many times a theorem) endows Hochschild cochains of a linear category with the structure of an $E_2$-algebra, that is, of an algebra over the little 2-disks operad. In this paper, we prove the cyclic Deligne conjecture, stating that for a linear category equipped with a Calabi-Yau structure (a kind of non-commutative orientation), the Hochschild cochains is endowed with the finer structure of a framed $E_2$-algebra, that is, of a circle-equivariant algebra over the little 2-disks operad. Our approach applies simultaneously to both smooth and proper linear categories, as well as to linear functors equipped with a relative Calabi-Yau structure, and works for a very general notion of linear category, including any dualizable presentable $\infty$-category. As a particular application, given a compact oriented manifold with boundary $\partial M \subset M$, our construction gives chain-level genus zero string topology operations on the relative loop homology $H_{*}(LM,L\partial M)$.

Discussion (0). Continue with ORCID 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. Noncommutative Cartier Formulae

    math.AT 2026-07 conditional novelty 8.0 of 10

    A noncommutative Cartier formula for E1-ring spectra is proven and applied to show that p-curvature of the quantum connection computes quantum Steenrod operations for Calabi-Yau symplectic manifolds.

  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. $\mathbb{E}_2$-algebra structures on the derived center of an algebraic scheme

    math.AT 2025-06 conditional novelty 5.0 of 10

    The Hochschild complex of an algebra or scheme is exhibited as the E1-operadic center of the structure sheaf, and the induced E2-algebra structure recovers the classical Gerstenhaber bracket and cup product.

  4. Calabi-Yau Deformation Quantization

    math.QA 2026-07 conditional novelty 3.0 of 10

    A Calabi-Yau version of Kontsevich's formality morphism is recorded, yielding canonical closed deformation quantizations for unimodular holomorphic Poisson Calabi-Yau manifolds.

Pith tools