论文标题
GKM歧管并不僵硬
GKM manifolds are not rigid
论文作者
论文摘要
我们在两个$ s^2 $ - 捆绑$ s^6 $的总空间上构建有效的GKM $ T^3 $ acTions，并在$ s^6 $的总空间上进行连接的稳定器，并带有相同的GKM图。这表明，具有连接稳定器的简单连接的整数GKM歧管的GKM图不能确定其同型类型。我们通过讨论此示例的最小值来补充这一点：Integer GKM歧管具有连接稳定器的同质类型的类型确实已在GKM图中编码，以较小的维度，较小的复杂性或较低的固定点数量。关于新示例上的几何结构，我们发现了一个几乎复杂的结构，该结构是在suptorus的作用下不变的。除了最小的例子外，我们还提供了一个类似的例子，其中圆环的作用是哈密顿量，这对哈密顿整数GKM歧管却不符合符合性的共同体学刚性。
We construct effective GKM $T^3$-actions with connected stabilizers on the total spaces of the two $S^2$-bundles over $S^6$ with identical GKM graphs. This shows that the GKM graph of a simply-connected integer GKM manifold with connected stabilizers does not determine its homotopy type. We complement this by a discussion of the minimality of this example: the homotopy type of integer GKM manifolds with connected stabilizers is indeed encoded in the GKM graph for smaller dimensions, lower complexity, or lower number of fixed points. Regarding geometric structures on the new example, we find an almost complex structure which is invariant under the action of a subtorus. In addition to the minimal example, we provide an analogous example where the torus actions are Hamiltonian, which disproves symplectic cohomological rigidity for Hamiltonian integer GKM manifolds.
