Shifted cotangent bundles, symplectic groupoids and deformation to the normal cone

2024/07/11 by Damien Calaque, Pavel Safronov, Calaque, Damien +1 · 4 citations
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2407.08622

Abstract

This article generalizes the theory of shifted symplectic structures to the relative context and non-geometric stacks. We describe basic constructions that naturally appear in this theory: shifted cotangent bundles and the AKSZ procedure. Along the way, we also develop the theory of shifted symplectic groupoids presenting shifted symplectic structures on quotients and define a deformation to the normal cone for shifted Lagrangian morphisms.

Cited by

• Multiplicative dimensional reduction
• Period sheaves via perverse pullbacks
• Shifted Symplectic Geometry by Examples
• Shifted Lagrangian thickenings of shifted Poisson derived schemes

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