Shifted symplectic Lie algebroids

Brent Pym, Pavel Safronov

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to) 7489–7557
Number of pages60
JournalInternational Mathematics Research Notices
Volume2020
Issue number21
DOIs
Publication statusPublished - 7 Sep 2018

Fingerprint

Dive into the research topics of 'Shifted symplectic Lie algebroids'. Together they form a unique fingerprint.

Cite this