Circle actions and suspension operations on smooth manifolds

Source abstract

Abstract 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 $S^{1}\times M$ yield two manifolds $\Sigma _{0}M$ and $\Sigma _{1}M$ , called the suspensions of M . These suspension operations play a fundamental role in the construction and classification of smooth manifolds admitting free circle actions. This paper presents corresponding results and supporting evidence.