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SHIFTED COISOTROPIC CORRESPONDENCES

Part of: Categories with structure Algebraic geometry: Foundations Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  03 July 2020

Rune Haugseng ,
Valerio Melani Open the ORCID record for Valerio Melani [Opens in a new window]  and
Pavel Safronov
Rune Haugseng
Affiliation:
Norwegian University of Science and Technology (NTNU), Trondheim, Norway (rune.haugseng@ntnu.no) URL: folk.ntnu.no/runegha
Valerio Melani
Affiliation:
Dipartimento di Matematica, Università di Pisa, Pisa, Italy (valerio.melani@unipi.it)
Pavel Safronov
Affiliation:
Institut für Mathematik, Universität Zürich, Zurich, Switzerland (pavel.safronov@math.uzh.ch)
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Abstract

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.

Keywords

derived algebraic geometryhigher categoriescoisotropic structures

MSC classification

Primary: 14A20: Generalizations (algebraic spaces, stacks)
Secondary: 17B63: Poisson algebras 18D05: Double categories, $2$-categories, bicategories and generalizations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 3 , May 2022 , pp. 785 - 849
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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Footnotes

The work of P.S. was supported by the NCCR SwissMAP grant of the Swiss National Science Foundation. R.H. received funding from grant IBS-R003-D1 of the Institute for Basic Science of the Republic of Korea.

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