Suspension

Summary

The suspension $SX$ of a topological space $X$ is the cylinder $X \times [0, 1]$ with each end collapsed to its own point. It looks like two cones on $X$ glued along their bases. The suspension of the $n$-sphere is the $(n+1)$-sphere, and suspension shifts reduced homology up by one degree. It is a basic construction in algebraic topology and stable homotopy theory.