论文标题
框架$ e_2 $浮子理论结构
Framed $E_2$ structures in Floer theory
论文作者
论文摘要
我们解决了构建框架（稳定）属的作用的长期问题 - $ 0 $ curves on Hamiltonian浮子理论；该歌地相当于框架$ e_2 $ operad。我们在以下一般环境中制定构造：我们将封闭的符号歧管的每个紧凑子集与支持的新的链级模型和支持，我们显示，我们显示，该模型在框架属的模量空间上携带了一个模型的动作。事实证明，这种构建对于子集的包含和符号构成组的作用非常有效。在一般环境中，我们呼吁虚拟基本链方法在特征$ 0 $的字段上构建操作，并在可以应用浮子的经典横向方法的特殊设置中，通过任意戒指给出一个单独的帐户。我们在Novikov环上执行所有构造，因此我们生成的代数结构与浮点理论中包含的定量信息兼容。在特征性$ 0 $的领域，我们的构造可以与作业理论中的结果结合在一起，以产生编码同型$ bv $代数的结构的明确操作。在附录中，我们解释了如何将论文的结果从封闭的符号歧管的类别扩展到几何界限。
We resolve the long-standing problem of constructing the action of the operad of framed (stable) genus-$0$ curves on Hamiltonian Floer theory; this operad is equivalent to the framed $E_2$ operad. We formulate the construction in the following general context: we associate to each compact subset of a closed symplectic manifold a new chain-level model for symplectic cohomology with support, which we show carries an action of a model for the chains on the moduli space of framed genus $0$ curves. This construction turns out to be strictly functorial with respect to inclusions of subsets, and the action of the symplectomorphism group. In the general context, we appeal to virtual fundamental chain methods to construct the operations over fields of characteristic $0$, and we give a separate account, over arbitrary rings, in the special settings where Floer's classical transversality approach can be applied. We perform all constructions over the Novikov ring, so that the algebraic structures we produce are compatible with the quantitative information that is contained in Floer theory. Over fields of characteristic $0$, our construction can be combined with results in the theory of operads to produce explicit operations encoding the structure of a homotopy $BV$ algebra. In an appendix, we explain how to extend the results of the paper from the class of closed symplectic manifolds to geometrically bounded ones.
