生成紧致环面簇的Fukaya范畴
辛几何
2023-08-10 v2
摘要
设X为紧致环面簇。X的量子上同调分解为直和，且与每个直和项Q相关联的是一个带秩1局部系统的环面纤维LQ。通过构造一个显式的类扭曲复形对象，我们证明在Q上Fukaya-Oh-Ohta-Ono的Kodaira-Spencer同构经由闭-开弦映射分解到LQ的Hochschild上同调中。我们推得后者为单射，从而（在假设Abouzaid判据的适当版本下）LQ分裂生成Fukaya范畴的相应直和项。
引用
@article{arxiv.1804.06386,
title = {Generating the Fukaya categories of compact toric varieties},
author = {Jack Smith},
journal= {arXiv preprint arXiv:1804.06386},
year = {2023}
}
备注
There are gaps in the discussion of the perturbation scheme in Section 3. The main results have subsequently been proved by different (better!) methods in arXiv:1910.01096 and arXiv:2308.03438