Viewing Einsteins 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 Einsteins theory to the vacuum and gauge covariant physical parts. We discuss the physical implications of our result in quantum gravity.
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