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arXiv · 2506.15210

Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem

Jakob Ulmer
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Abstract

We relate graph complexes, Calabi-Yau $A_\infty$-categories and Kontsevich's cocycle construction. Our main result produces a commutative square of shifted Poisson algebras; one of its edges is the Loday-Quillen-Tsygan map, generalized to $A_\infty$-categories. We describe a quantized version via Beilinson-Drinfeld algebras. The larger context is to provide categorical methods which relate enumerative geometry (as in mirror symmetry) and large $N$ gauge theories.

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BibTeXRIS

Jakob Ulmer. 2025-06-18. Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem. https://arxiv.org/abs/2506.15210

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