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arXiv · 2610.07195

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

Sergei A. Merkulov
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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 ${\mathcal M}:=M\times Πg$, $g$ 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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Sergei A. Merkulov. 2026-10-05. Homotopy Poisson and BV$_\infty$ structures on derived moduli spaces of flat connections. https://arxiv.org/abs/2610.07195

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