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Homotopy Poisson and BV$_\infty$ structures on derived moduli spaces of flat connections

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Sergei A. Merkulov

Differential Geometry · Submitted 5 Oct 2026

abstract compiled · 2026-10-07 · no language-model review

The authors' main claim We show that quasi-Poisson and quasi-BV structures on (super)manifolds $M$ admitting an action of a Lie (super)group $G$ can be identified with a special class of homotopy Poisson and respectively $BV_\infty$ structures on the associated differential (super)manifolds of the form ${\mathcal M}:=M\times \Pi g$, $g$ being the Lie (super)algebra of $G$.

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arXiv ID2610.07195 (version 1)
Pith IDDALBXLN6, Pith's permanent record of this paper and its review
CitationSergei A. Merkulov. "Homotopy Poisson and BV$_\infty$ structures on derived moduli spaces of flat connections." arXiv:2610.07195 (2026). https://pith.science/paper/DALBXLN6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-07: 1 request, 3,153 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.19 · mentions code or data availability 0.02.

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We show that quasi-Poisson and quasi-BV structures on (super)manifolds $M$ admitting an action of a Lie (super)group $G$ can be identified with a special class of homotopy Poisson and respectively $BV_\infty$ structures on the associated differential (super)manifolds of the form ${\mathcal M}:=M\times \Pi g$, $g$ being the Lie (super)algebra of $G$. The construction is based on the proven existence of an essentially unique family of higher Jacobiators for any Lie (super)algebra $g$ with an invariant (odd or even) scalar product. We apply these arguments to the moduli spaces $M$ of flat $G$-connections on a surface with boundaries using Fock-Rosly construction.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that quasi-Poisson and quasi-BV structures on (super)manifolds $M$ admitting an action of a Lie (super)group $G$ can be identified with a special class of homotopy Poisson and respectively $BV_\infty$ structures on the associated differential (super)manifolds of the form ${\mathcal M}:=M\times \Pi g$, $g$ being the Lie (super)algebra of $G$. result 0.86 0.93 0.85 asserted 1.00
s1 The construction is based on the proven existence of an essentially unique family of higher Jacobiators for any Lie (super)algebra $g$ with an invariant (odd or even) scalar product. method 0.87 0.67 0.07 asserted 1.00
s2 We apply these arguments to the moduli spaces $M$ of flat $G$-connections on a surface with boundaries using Fock-Rosly construction. contribution 0.76 0.84 0.09 asserted 0.99

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Original abstract

We show that quasi-Poisson and quasi-BV structures on (super)manifolds $M$ admitting an action of a Lie (super)group $G$ can be identified with a special class of homotopy Poisson and respectively $BV_\infty$ structures on the associated differential (super)manifolds of the form ${\mathcal M}:=M\times \Pi g$, $g$ being the Lie (super)algebra of $G$. The construction is based on the proven existence of an essentially unique family of higher Jacobiators for any Lie (super)algebra $g$ with an invariant (odd or even) scalar product. We apply these arguments to the moduli spaces $M$ of flat $G$-connections on a surface with boundaries using Fock-Rosly construction.

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