The Arnold-Givental conjecture and moment Floer homology
The Arnold-Givental conjecture and moment Floer homology
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阿诺德-吉文塔尔猜想和弗洛尔矩同调
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发表时间：
2003
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通讯作者：
U. Frauenfelder
中科院分区：
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作者：
U. Frauenfelder
证明了一类反辛对合的不动点集的Marsden-Weinstein对偶中的Lagrange子流形的Arnold-Givental猜想。对于这些拉格朗日的弗洛尔同调不能在一般情况下定义的标准手段，由于冒泡现象。为了克服这一困难，我们考虑矩Floer同调，其边界算子是通过计算具有更好的紧致性比原来的Floer方程的带上的辛涡方程的解决方案。
We prove the Arnold-Givental conjecture for a class of Lagrangian submanifolds in Marsden-Weinstein quotients which are fixpoint sets of some antisymplectic involution. For these Lagrangians the Floer homology cannot in general be defined by standard means due to the bubbling phenomenon. To overcome this difficulty we consider moment Floer homology whose boundary operator is defined by counting solutions of the symplectic vortex equations on the strip which have better compactness properties than the original Floer equations.