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• W2953048332 abstract "We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L subset X$ with a bounding chain. Simultaneously, we define the quantum cohomology algebra of $X$ relative to $L$ and prove its associativity. We also define the relative quantum connection and prove it is flat. A wall-crossing formula is derived that allows the interchange of point-like boundary constraints and certain interior constraints in open Gromov-Witten invariants. Another result is a vanishing theorem for open Gromov-Witten invariants of homologically non-trivial Lagrangians with more than one point-like boundary constraint. In this case, the open Gromov-Witten invariants with one point-like boundary constraint are shown to recover certain closed invariants. From open WDVV and the wall-crossing formula, a system of recursive relations is derived that entirely determines the open Gromov-Witten invariants of $(X,L) = (mathbb{C}P^n, mathbb{R}P^n)$ with $n$ odd, defined in previous work of the authors. Thus, we obtain explicit formulas for enumerative invariants defined using the Fukaya-Oh-Ohta-Ono theory of bounding chains." @default.
• W2953048332 created "2019-06-27" @default.
• W2953048332 creator A5027731276 @default.
• W2953048332 creator A5032753665 @default.
• W2953048332 date "2023-06-07" @default.
• W2953048332 modified "2023-10-01" @default.
• W2953048332 title "Relative quantum cohomology" @default.
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• W2953048332 doi "https://doi.org/10.4171/jems/1337" @default.
• W2953048332 hasPublicationYear "2023" @default.
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