2022/11/10 by Or Kedar, Jake P. Solomon, Kedar, Or +1
Mathematics · #53D12 #53D37 #53D40 (Primary) 55N25 #58J32 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2211.05439
openalex publication_date 2022/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L⊂ X be a not necessarily orientable relatively Pin Lagrangian submanifold in a symplectic manifold X. We construct a family of cyclic unital curved A_∞ structures on differential forms on L with values in the local system of graded non-commutative rings given by the tensor algebra of the orientation local system of L. The family of A_∞ structures is parameterized by the cohomology of X relative to L and satisfies properties analogous to the axioms of Gromov-Witten theory. On account of the non-orientability of L, the evaluation maps of moduli spaces of J-holomorphic disks with boundary in L may not be relatively orientable. To deal with this problem, we use recent results on orientor calculus.