A∞-structure for Lines in a Plane
نویسنده
چکیده
As an explicit example of an A∞-structure associated to geometry, we construct an A∞-structure for a Fukaya category of finitely many lines (Lagrangians) in R , i.e., we define also non-transversal A∞-products. This construction is motivated by homological mirror symmetry of (two-)tori, where R is the covering space of a two-torus. The strategy is based on an algebraic reformulation of Morse homotopy theory through homological perturbation theory (HPT) as discussed by Kontsevich and Soibelman in [21], where we introduce a special DG category which is a key idea of our construction.
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