A Gysin sequence for semifree actions of 𝑆³

Abstract

In this work we shall consider smooth semifree (i.e., free outside the fixed point set) actions of S 3 {{\mathbf {S}}^3} on a manifold M M . We exhibit a Gysin sequence relating the cohomology of M M with the intersection cohomology of the orbit space M / S 3 M/{{\mathbf {S}}^3} . This generalizes the usual Gysin sequence associated with a free action of S 3 {{\mathbf {S}}^3} .