The Gysin sequence for ${\mathbb S}^3$-actions on manifolds

TL;DR

This paper constructs a Gysin sequence for smooth ${ m S}^3$-actions on manifolds, providing a new algebraic tool to analyze the topology of manifolds with such symmetries.

Contribution

It introduces a Gysin sequence specifically tailored for ${ m S}^3$-actions, extending existing methods to this class of group actions.

Findings

Provides a new algebraic sequence for ${ m S}^3$-actions

Enables analysis of manifold topology under ${ m S}^3$-symmetries

Lays groundwork for future topological studies of ${ m S}^3$-equivariant manifolds

Abstract

We construct a Gysin sequence associated to any smooth ${\mathbb S}^3$-action on a smooth manifold.