去除退化复切及相关同伦和同调群的一个拓扑障碍
A Topological Obstruction to the Removal of a Degenerate Complex Tangent and Some Related Homotopy and Homology Groups
摘要：
在这篇文章中，我们推导出一个拓扑障碍，以消除一个孤立的退化复杂的切线嵌入到$\mathbb{C}^3$的3-流形（不影响其余的复杂切线的结构）。我们演示了如何消失的障碍是一个充要条件和充分条件（本地）去除孤立的复切线。障碍物是由$\mathbb{C}^3$（= $\mathbb{R}^6$）中的实3-平面的Grassmanian中的全实3-平面组成的空间$\mathbb{Y}$的某个同伦类。我们进一步计算额外的同伦和同调群的空间$\mathbb{Y}$和它的补充$\mathbb{W}$组成的“部分复杂的”3-平面在$\mathbb{C}^3$。
英文摘要：
In this article, we derive a topological obstruction to the removal of a isolated degenerate complex tangent to an embedding of a 3-manifold into $\mathbb{C}^3$ (without affecting the structure of the remaining complex tangents). We demonstrate how the vanishing of this obstruction is both a necessary and sufficient condition for the (local) removal of the isolated complex tangent. The obstruction is a certain homotopy class of the space $\mathbb{Y}$ consisting of totally real 3-planes in the Grassmanian of real 3-planes in $\mathbb{C}^3$ (=$\mathbb{R}^6$). We further compute additional homotopy and homology groups for the space $\mathbb{Y}$ and of its complement $\mathbb{W}$ consisting of "partially complex" 3-planes in $\mathbb{C}^3$.
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