论文标题
用于虚拟链的公理方法
An axiomatic approach to virtual chains
论文作者
论文摘要
我们介绍了Kuranishi演示的类别，其对象是Fukaya和Ono引入的Kuranishi结构的变体，并且可以看作是Pardon研究的版本的完善。然后，我们将虚拟链的概念明确地作为从该类别到链复合物类别的两个函子之间的自然转换。我们将这样的基准称为“虚拟计数理论”。为了证明该定义具有非平凡的内容，我们然后构建了一个多材料，其对象是kuranishi流量类别，并表明虚拟计数的理论确定了链复合物多材的多函数。然后，我们在汉密尔顿浮子理论的设置中实施了这一构建，从与Groman和Varolgunes的某些联合合作中借用，从而产生了汉密尔顿浮动组（以及对它们的操作）的构造，作为该机器的输出。我们计划在随后的联合工作中为拉格朗日花车理论提供类似的说法。
We introduce a category of Kuranishi presentations, whose objects are a variant of the Kuranishi structures introduced by Fukaya and Ono, and which can be seen as a refinement of the version studied by Pardon. We then formulate the notion of virtual chains categorically as a natural transformation between two functors from this category to the category of chain complexes; we call such a datum 'a theory of virtual counts'. To show that this definition carries non-trivial content, we then construct a multicategory whose objects are Kuranishi flow categories, and show that a theory of virtual counts determines a multifunctor to the multicategory of chain complexes. We then implement this construction in the setting of Hamiltonian Floer theory, borrowing from some joint work with Groman and Varolgunes, yielding a construction of Hamiltonian Floer groups (and operations on them) as an output of this machine. We plan to provide a similar account for Lagrangian Floer theory in subsequent joint work.
