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تسجيل مستخدم جديدA Double Poisson Algebra Structure on Fukaya Categories
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Let $M$ be an exact symplectic manifold with $c_1(M)=0$. Denote by $mathrm{Fuk}(M)$ the Fukaya category of $M$. We show that the dual space of the bar construction of $mathrm{Fuk}(M)$ has a differential graded noncommutative Poisson structure. As a corollary we get a Lie algebra structure on the cyclic cohomology $mathrm{HC}^bullet(mathrm{Fuk}(M))$, which is analogous to the ones discovered by Kontsevich in noncommutative symplectic geometry and by Chas and Sullivan in string topology.
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