  In this paper the relations between the existence of Lagrangian fibration of
Hyper-K\"{a}hler manifolds and the existence of the Large Radius Limit is
established. It is proved that if the the rank of the second homology group of
a Hyper-K\"{a}hler manifold N of complex dimension $2n\geq4$ is at least 5,
then there exists an unipotent element T in the mapping class group $\Gamma
$(N) such that its action on the second cohomology group satisfies
$(T-id)^{2}\neq0$ and $(T-id)^{3}=0.$ A Theorem of Verbitsky implies that the
symmetric power $S^{n}(T)$ acts on $H^{2n}$ and it satisfies $(S^{n}%
(T)-id)^{2n}\neq0$ and $(S^{n}(T)-id)^{2n+1}=0.$ This fact established the
existence of Large Radius Limit for Hyper-K\"{a}hler manifolds for polarized
algebraic Hyper-K\"{a}hler manifolds. Using the theory of vanishing cycles it
is proved that if a Hyper-K\"{a}hler manifold admits a Lagrangian fibration
then the rank of the second homology group is greater than or equal to five. It
is also proved that the fibre of any Lagrangian fibration of a Hyper-K\"{a}hler
manifold is homological to a vanishing invariant $2n$ cycle of a maximal
unipotent element acting on the middle homology. According to Clemens this
vanishing invariant cycle can be realized as a torus. I conjecture that the SYZ
conjecture implies finiteness of the topological types of Hyper-K\"{a}hler
manifolds of fix dimension.
