What question did this study set out to answer?

August 1, 2026Differential Geometry and its Applications17 citationsOpen Access

An outline of shifted Poisson structures and deformation quantisation in derived differential geometry

Key Points

This work aims to translate results from derived algebraic geometry to derived differential geometry, focusing on shifted Poisson structures.
Discussed various structures including NQ-manifolds and smooth stacks.
Examined existence and classification of deformation quantisations on these structures.
Identified connections between shifted Poisson structures and deformation quantisations.
Provided frameworks to categorize these structures in derived differential geometry.

Abstract

We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.

问 AI

Bookmark

View Full Paper