Shifted symplectic Lie algebroids
| Autor: | Pavel Safronov, Brent Pym |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Topological quantum field theory General Mathematics Homotopy 010102 general mathematics Pontryagin class Algebraic geometry 01 natural sciences Mathematics - Algebraic Geometry Tensor product Differential Geometry (math.DG) Differential geometry Mathematics - Symplectic Geometry Homogeneous space FOS: Mathematics Symplectic Geometry (math.SG) 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Symplectic geometry Mathematics |
| Zdroj: | International Mathematics Research Notices Pym, B & Safronov, P 2018, ' Shifted symplectic Lie algebroids ', International Mathematics Research Notices, vol. 2020, no. 21, pp. 7489–7557 . https://doi.org/10.1093/imrn/rny215 |
| DOI: | 10.1093/imrn/rny215 |
| Popis: | Shifted symplectic Lie and $L_\infty$ 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 $\Omega^2$-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 $C^\infty$, holomorphic and algebraic settings, and are based on a number of technical results on the homotopy theory of $L_\infty$ algebroids and their differential forms, which may be of independent interest. Comment: 58 pages |
| Databáze: | OpenAIRE |
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