论文标题
无限尺寸中的均值图的正常形式
Normal form of equivariant maps in infinite dimensions
论文作者
论文摘要
建立了无限二维流形之间平滑的均值图的局部正常形式定理。这些正常形式的结果即使在有限维度中也是新的。该证明的灵感来自动力学系统的Lyapunov-Schmidt还原和模量空间的Kuranishi方法。它使用切片定理将fréchet歧管作为主要技术工具。结果，通过对相对于小组作用进行分配的级别映射图获得的抽象模量空间带有kuranishi空间的结构，即，这样的模量空间是通过平滑地图的零组的紧凑组在商上局部建模的。一般结果应用于反二键式激体的模量空间，塞伯格（Seiberg）的模量空间和模态曲线的模量空间。
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the Lyapunov-Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces. It uses a Slice Theorem for Fréchet manifolds as the main technical tool. As a consequence, the abstract moduli space obtained by factorizing a level set of the equivariant map with respect to the group action carries the structure of a Kuranishi space, i.e., such moduli spaces are locally modeled on the quotient by a compact group of the zero set of a smooth map. The general results are applied to the moduli space of anti-self-dual instantons, the Seiberg-Witten moduli space and the moduli space of pseudoholomorphic curves.
