Circle actions and suspension operations on smooth manifolds
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 180
- Issue
- 3
- Pages
- 643–662
- Publication date
- 19 January 2026
- Language
- EN