تقرير
The K\'unneth theorem for the Fukaya algebra of a product of Lagrangians
| العنوان: | The K\'unneth theorem for the Fukaya algebra of a product of Lagrangians |
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| المؤلفون: | Amorim, Lino |
| المصدر: | Internat. J. Math. 28 (2017), no. 4, 1750026, 38 pp |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry |
| الوصف: | Given a compact Lagrangian submanifold $L$ of a symplectic manifold $(M,\omega)$, Fukaya, Oh, Ohta and Ono construct a filtered $A_\infty$-algebra $\mathcal{F}(L)$, on the cohomology of $L$, which we call the Fukaya algebra of $L$. In this paper we describe the Fukaya algebra of a product of two Lagrangians submanifolds $L_1\times L_2$. Namely, we show that $\mathcal{F}(L_1\times L_2)$ is quasi-isomorphic to $\mathcal{F}(L_1)\otimes_\infty \mathcal{F}(L_2)$, where $\otimes_\infty$ is the tensor product of filtered $A_\infty$-algebras defined in arXiv:1404.7184. As a corollary of this quasi-isomorphism we obtain a description of the bounding cochains on $\mathcal{F}(L_1\times L_2)$ and of the Floer cohomology of $L_1\times L_2$. Comment: v2: one mistake fixed; to appear in International Journal of Mathematics |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1142/S0129167X17500264 |
| URL الوصول: | http://arxiv.org/abs/1407.8436 |
| رقم الأكسشن: | edsarx.1407.8436 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1142/S0129167X17500264 |
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