  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 $\mathbb{C}^3$.
