论文标题
渐近的圆锥形calabi-Yau和G2歧管的拓扑结构，以及几乎Kähler和几乎G2 Conifolds的拓扑。
Topology of asymptotically conical Calabi--Yau and G2 manifolds and desingularization of nearly Kähler and nearly G2 conifolds
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
A natural approach to the construction of nearly G2 manifolds lies in resolving nearly G2 spaces with isolated conical singularities by gluing in asymptotically conical G2 manifolds modelled on the same cone. If such a resolution exits, one expects there to be a family of nearly G2 manifolds, whose endpoint is the original nearly G2 conifold and whose parameter is the scale of the glued in asymptotically conical G2 manifold. We show that in many cases such a curve does not exist. The non-existence result is based on a topological result for asymptotically conical G2 manifolds: if the rate of the metric is below -7/2, then the G2 4-form is exact if and only if the manifold is isometric to the 7-dimensional Euclidean space. A similar construction is possible in the nearly Kähler case, which we investigate in the same manner with similar results. In this case, the non-existence results is based on a topological result for asymptotically conical Calabi--Yau 6-manifolds: if the rate of the metric is below -3, then the square of the Kähler form and the complex volume form can only be simultaneously exact, if the manifold is isometric to the 6-dimensional Euclidean space.
