具有沿圆的结点奇点的G $_2$流形
G$_2$ manifolds with nodal singularities along circles
摘要：
利用扭连通和方法构造了一个具有G $_2$完整性和圆上节点奇点的紧致流形。本文通过求解Calabi猜想找到了某些渐近圆柱形流形上的节点奇点的匹配积木。然而，通过与无扭连通和的情况相比，我们发现奇异扭连通和构造的障碍空间是无穷维的。通过对阻塞项的分析，证明了进一步的胶合可以解决阻塞问题，从而得到一个具有$_2$完整性的紧致流形和一个具有连接$\mathbb{S}^3\times\mathbb{S}^3$的孤立锥奇点.
英文摘要：
The goal of this paper is the construction of a compact manifold with G$_2$ holonomy and nodal singularities along circles using twisted connected sum method. This paper finds matching building blocks by solving the Calabi conjecture on certain asymptotically cylindrical manifolds with nodal singularities. However, by comparison to the untwisted connected sum case, it turns out that the obstruction space for the singular twisted connected sum construction is infinite dimensional. By analyzing the obstruction term, there are strong evidences that the obstruction may be resolved if a further gluing is performed in order to get a compact manifold with G$_2$ holonomy and isolated conical singularities with link $\mathbb{S}^3\times\mathbb{S}^3$.
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