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Homotopy Poisson and BV∞ structures on derived moduli spaces of flat connections
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∞ structures on the associated differential (super)manifolds of the form ℳ:=M× 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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BibTeX
@misc{merkulov2026homotopy,
title = {{Homotopy Poisson and BV$_\infty$ structures on derived moduli spaces of flat connections}},
author = {Sergei A. Merkulov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07195},
eprint = {2610.07195},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07195},
}
RIS
TY - UNPB
TI - Homotopy Poisson and BV_∞ structures on derived moduli spaces of flat connections
AU - Sergei A. Merkulov
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07195
UR - https://arxiv.org/abs/2610.07195
AB - 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_∞ structures on the associated differential (super)manifolds of the form ℳ:=M× 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.
ER -