Derived coisotropic structures I: affine case

Valerio Melani, Pavel Safronov

Research output: Contribution to journalArticlepeer-review


We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. Pn-algebras. Roughly speaking, a coisotropic morphism is given by a Pn+1-algebra acting on a Pn-algebra. One of our main results is an identification of the space of such coisotropic structures with the space of Maurer--Cartan elements in a certain dg Lie algebra of relative polyvector fields. To achieve this goal, we construct a cofibrant replacement of the operad controlling coisotropic morphisms by analogy with the Swiss-cheese operad which can be of independent interest. Finally, we show that morphisms of shifted Poisson algebras are identified with coisotropic structures on their graph.
Original languageEnglish
Pages (from-to)3061-3118
Number of pages49
JournalSelecta Mathematica (New Series)
Early online date9 Mar 2018
Publication statusPublished - 30 Sep 2018


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