Finite approximation of path space.

Question

Let $M$ be a connected Riemannian manifold, $\Omega(M)=\Omega$ the path space and $E: \Omega \to \mathbb{R}$ the energy function. We can define $\Omega^c:=E^{-1}([0,c])$ and $\Omega(t_0, \dots, t_k)$ the subspace of $\Omega$ consisting of paths $\omega: [0,1] \rightarrow M$ such that $\omega(0)=p$ and $\omega(1)=q$ and $\omega|[t_{i-1},t_i]$ is a geodesic far all $i \in [1,k]$. So we can prove that the subspace (Milnor, Morse theory notation) $\mathrm{Int\ }\Omega(t_0, \cdots, t_k)^c:=(\mathrm{Int\ } \Omega^c) \cap \Omega(t_0, \cdots, t_k)$ is a finite dimensional approximation of $\Omega$ and its dimension is $\dim(M)(k-1)$. If $B$ is the restriction of $E$ to $\mathrm{Int\ } \Omega(t_0, \cdots, t_k)^c$, $B^c=E^{-1}([0])$ is a manifold? How can i prove that for large values of $c$ every critical point in $B-B^0$ has index $\ge \lambda_0$?