  Viewing Einstein's theory as the gauge theory of Lorentz group, we construct
the most general vacuum connections which have vanishing curvature tensor and
show that the vacuum space-time can be classified by the knot topology
$\pi_3(S^3)\simeq \pi_3(S^2)$ of $\pi_3(SO(3,1))$. With this we obtain the
gauge independent vacuum decomposition of Einstein's theory to the vacuum and
gauge covariant physical parts. We discuss the physical implications of our
result in quantum gravity.
