2007/03/06 by Hiroshige Kajiura, Kajiura, Hiroshige
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #hep-th #math.QA #math.SG
paper · pdf · doi:10.48550/arxiv.math/0703164
28 pages
arxiv created 2007/03/06 · arxiv updated 2009/12/01
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 \R2, ie., we define also \em non-transversal A_∞-products. This construction is motivated by homological mirror symmetry of (two-)tori, where \R2 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 math.SG/0011041, where we introduce a special DG category which is a key idea of our construction.