  Let $M$ be a smooth manifold with $\dim M\geq 3$ and a base point $x_{0}$.
Surgeries along the oriented circle $S^{1}\times \{x_{0}\}$ on the product $
S^{1}\times M$ yields two manifolds $\Sigma _{0}M$ and $\Sigma _{1}M$, called
the suspensions of $M$.
  The suspension operations $\Sigma _{i}$ play a basic role in the construction
and classification of the smooth manifolds which admit free $ S^{1}$-actions.
We illustrate this by a number of applications.
