تقرير
The Fukaya $A_\infty$ algebra of a non-orientable Lagrangian
| العنوان: | The Fukaya $A_\infty$ algebra of a non-orientable Lagrangian |
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| المؤلفون: | Kedar, Or, Solomon, Jake P. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, High Energy Physics - Theory, Mathematics - Algebraic Geometry, 53D37, 53D40 (Primary) 55N25, 53D12, 58J32 (Secondary) |
| الوصف: | Let $L\subset X$ be a not necessarily orientable relatively $Pin$ Lagrangian submanifold in a symplectic manifold $X$. We construct a family of cyclic unital curved $A_\infty$ 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 $A_\infty$ 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. Comment: 58 pages, includes summary of relevant background from arXiv:2211.05117 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2211.05439 |
| رقم الأكسشن: | edsarx.2211.05439 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |