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coisotropic structures

Journal of the Institute of Mathematics of Jussieu (1)

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SHIFTED COISOTROPIC CORRESPONDENCES
Part of
Rune Haugseng, Valerio Melani, Pavel Safronov
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 3 / May 2022

Published online by Cambridge University Press:

03 July 2020, pp. 785-849

Print publication:

May 2022
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We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks, where the $i$-morphisms are given by $i$-fold coisotropic correspondences. Assuming an expected equivalence of different models of higher Morita categories, we prove that all derived Poisson stacks are fully dualizable and so determine framed extended TQFTs by the Cobordism Hypothesis. Along the way, we also prove that the higher Morita category of $E_{n}$-algebras with respect to coproducts is equivalent to the higher category of iterated cospans.