  In this paper we determine the cosmological constant as a topological
invariant by applying certain techniques from low dimensional differential
topology. We work with a small exotic $R^{4}$ which is embedded into the
standard $\mathbb{R}^{4}$. Any exotic $R^4$ is a Riemannian smooth manifold
with necessary non-vanishing curvature tensor. To determine the invariant part
of such curvature we deal with a canonical construction of $R^4$ where it
appears as a part of the complex surface $K3\#\overline{CP(2)}$. Such $R^{4}$'s
admit hyperbolic geometry. This fact simplifies significantly the calculations
and enforces the rigidity of the expressions. In particular, we explain the
smallness of the cosmological constant with a value consisting of a combination
of (natural) topological invariant. Finally, the cosmological constant appears
to be a topologically supported quantity.
