论文标题
部分可观测时空混沌系统的无模型预测
The GKM correspondence in dimension 6
论文作者
论文摘要
从GKM的同学共同体描述来看，GKM歧管的GKM图具有自由的eprovariant图共同体，并满足了庞加莱的二元状态。我们证明，对于抽象$ 3 $ valent $ t^2 $ gkm图，这些条件就足够了，可以通过简单连接的$ 6 $维二维GKM歧管实现。我们的意识到有限各向同性组的任何闭合层都包含一个固定点。此外，我们认为，如果存在一个固定点，在该固定点附近发生，最多有两个不同的有限的非平地各向同性组，那么实现的实现是独一无二的，直到同型同态性，因此建立了一个复杂性的一gkm对应关系，以$ 6 $ 6 $。我们表明，关于唯一唯一性的陈述是错误的，没有两个条件在有限的各向同性的情况下，通过在有固定点的情况下提供反反例，其中包括三个不同的邻近有限的各向同性组，以及一个简单连接的整数GKM歧管，并具有没有任何固定点的封闭式同位素组的封闭层。
It follows from the GKM description of equivariant cohomology that the GKM graph of a GKM manifold has free equivariant graph cohomology, and satisfies a Poincaré duality condition. We prove that these conditions are sufficient for an abstract $3$-valent $T^2$-GKM graph to be realizable by a simply-connected $6$-dimensional GKM manifold. Our realization has the property that any closed stratum of a finite isotropy group contains a fixed point. Furthermore, we argue that in case there exists a fixed point in whose vicinity there occur at most two distinct finite nontrivial isotropy groups such a realization is unique up to equivariant homeomorphism, thus establishing a complexity one GKM correspondence in dimension $6$. We show that the statement on equivariant uniqueness is false without the two conditions on the finite isotropies by providing counterexamples in presence of a fixed point with three distinct neighbouring finite isotropy groups, as well as an example of a simply-connected integer GKM manifold with a closed stratum of a finite isotropy group which does not contain any fixed point.
