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arXiv · 1608.01482

Derived coisotropic structures I: affine case

Valerio Melani·Pavel Safronov
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Abstract

We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras. Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting on a $P_n$-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.

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Valerio Melani, Pavel Safronov. 2016-08-04. Derived coisotropic structures I: affine case. https://doi.org/10.1007/s00029-018-0406-2

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