  We present a topological classification of vacuum space-time. Assuming the
3-dimensional space allows a global chart, we show that the static vacuum
space-time of Einstein's theory can be classified by the knot topology
$\pi_3(S^3)=\pi_3(S^2)$. Viewing Einstein's theory as a gauge theory of Lorentz
group and identifying the gravitational connection as the gauge potential of
Lorentz group, we construct all possible vacuum gravitational connections which
give a vanishing curvature tensor. With this we show that the vacuum connection
has the knot topology, the same topology which describes the multiple vacua of
SU(2) gauge theory. We discuss the physical implications of our result in
quantum gravity.
