تقرير
Relative quantum cohomology
| العنوان: | Relative quantum cohomology |
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| المؤلفون: | Solomon, Jake P., Tukachinsky, Sara B. |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, High Energy Physics - Theory, Mathematics - Algebraic Geometry, 53D45, 53D37 (Primary), 14N35, 14N10, 53D12 (Secondary) |
| الوصف: | 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. Comment: 70 pages, 9 figures; corrected minor errors, updated bibliography |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.4171/jems/1337 |
| URL الوصول: | http://arxiv.org/abs/1906.04795 |
| رقم الأكسشن: | edsarx.1906.04795 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.4171/jems/1337 |
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