تقرير
Categorical primitive forms of Calabi-Yau $A_\infty$-categories with semi-simple cohomology
| العنوان: | Categorical primitive forms of Calabi-Yau $A_\infty$-categories with semi-simple cohomology |
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| المؤلفون: | Amorim, Lino, Tu, Junwu |
| المصدر: | Selecta Math. (N.S.) 28 (2022), no. 3, Paper No. 54, 44 pp |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, Mathematics - Algebraic Geometry, Mathematics - K-Theory and Homology |
| الوصف: | We study categorical primitive forms for Calabi--Yau $A_\infty$ categories with semi-simple Hochschild cohomology. We classify these primitive forms in terms of certain grading operators on the Hochschild homology. We use this result to prove that, if the Fukaya category ${{\sf Fuk}}(M)$ of a symplectic manifold $M$ has semi-simple Hochschild cohomology, then its genus zero Gromov--Witten invariants may be recovered from the $A_\infty$-category ${{\sf Fuk}}(M)$ together with the closed-open map. An immediate corollary of this is that in the semi-simple case, homological mirror symmetry implies enumerative mirror symmetry. Comment: Comments welcome. v2: sign corrections and other improvements. v3: some improvements |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00029-022-00769-z |
| URL الوصول: | http://arxiv.org/abs/1909.05319 |
| رقم الأكسشن: | edsarx.1909.05319 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00029-022-00769-z |
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