Circle actions and Suspension operations on Smooth manifolds

Abstract

Let $M$ be a smooth manifold with $\dim M\ge 3$ 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 $\hat{I}{\pounds }_{0}M$ and $\hat{I}{\pounds }_{1}M$, called the suspensions of $M$. The suspension operations $\hat{I}{\pounds }_i$ 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.

22pages