Maurer-Cartan deformation of Lagrangians

Abstract

The Maurer-Cartan algebra of a Lagrangian LL is the algebra that encodes the deformation of the Floer complex CF(L,L;Ξ›)CF(L,L;\Lambda) as an A∞A_\infty-algebra. We identify the Maurer-Cartan algebra with the 00-th cohomology of the Koszul dual dga of CF(L,L;Ξ›)CF(L,L;\Lambda). Making use of the identification, we prove that there exists a natural isomorphism between the Maurer-Cartan algebra of LL and a certain analytic completion of the wrapped Floer cohomology of another Lagrangian GG when GG is \emph{dual} to LL in the sense to be defined. In view of mirror symmetry, this can be understood as specifying a local chart associated with LL in the mirror rigid analytic space. We examine the idea by explicit calculation of the isomorphism for several interesting examples.Comment: 51 pages, 12 figures. Comments are welcom

    Similar works

    Full text

    thumbnail-image

    Available Versions