辛不变量与代数结构

本项目包含两个方面: .一、研究 Fukaya 范畴和辛场论、辛同调之间的关系。特别地，研究 Fukaya 范畴的 Hochschild 上同调或循环上同调、辛同调、等变辛同调和 filled 线性化切触同调等的代数结构，以及它们相互间的关系。在这方面研究的进展，将会对辛场论、辛同调、Fukaya 范畴、拓扑场论和同调镜对称猜测等许多问题的研究产生推动作用。.二、针对 Fukaya 范畴和线性化切触同调涉及的模空间的横截性问题，利用 virtual 邻域技术，给出严格且比较起来更简捷的构造，最终完成以前的研究计划。在这方面研究的进展，将会对 Fukaya 范畴和辛场论等领域的研究产生推动作用。

This project consists of two parts:.1, Studying the relationships between Fukaya categories and symplectic homology or symplectic field theory. In particular, we plan to study the algebraic structures on Hochschild cohomology, symplectic homology, equivariant symplectic homology, filled linearized contact homology, etc., and the inter-relationships among them..2, We will study the transversality problem of moduli spaces related to the Fukaya category and the linearized contact homology. By applying the virtual neighborhood techniques, we will give a rigorous and much more concise construction. A previous project which studies the relationship between Fukaya category and symplectic field theory will be finished. The advances in this aspect will push forward these related research fields.