This paper introduces quantum bv algebras and their implications in homotopy geometry, highlighting key properties.
We introduce the concept of a quantum BV L∞-algebra and study fundamental properties. In particular, we investigate homotopy Lie theoretic structures that naturally arise in the context of Chern-Simons theory. Of note, are the notions of homotopy BV data and of a BV orientation. The sequel of this paper will involve the direct application of these constructions to the setting of Chern-Simons theory.
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Elliot Cheung (2025) studied this question.
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