多重褶皱与广义Fredholm理论
Polyfolds And A General Fredholm Theory
摘要：
我们调查一个非常普遍的（非线性）Fredholm理论的一类新的环境空间，称为polyfolds。这个理论目前正在与K. Wysocki和E.桑德这些新空间的基本特征是，一般来说，它们可能具有局部变化的维数。这些新的空间是需要一个功能分析处理的非线性问题，涉及分析的极限行为。该理论适用于Gromov-Witten和Floer理论以及辛域论。
英文摘要：
We survey a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. This theory is being currently developed jointly with K. Wysocki and E. Zehnder. The basic feature of these new spaces is that in general they may have locally varying dimensions. These new spaces are needed for a functional analytic treatment of nonlinear problems involving analytic limiting behavior. This theory is applicable to Gromov-Witten and Floer Theory as well as Symplectic Field Theory.
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