2016/12/30 by Pym, Brent, Safronov, Pavel · 2 citations
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1612.09446
Shifted symplectic Lie and L_∞ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify zero-, one- and two-shifted symplectic algebroids and their higher gauge symmetries, in terms of classical geometric "higher structures", such as Courant algebroids twisted by Ω2-gerbes. As applications, we produce new examples of twisted Courant algebroids from codimension-two cycles, and we give symplectic interpretations for several well known features of higher structures (such as twists, Pontryagin classes, and tensor products). The proofs are valid in the C^∞, holomorphic and algebraic settings, and are based on a number of technical results on the homotopy theory of L_∞ algebroids and their differential forms, which may be of independent interest.