8-dimensional manifolds with \(S^3\times S^3\) actions (Q5939006)

The author studies the action of \(S^3\times S^3\) on closed, orientable, smooth 8-manifolds. The paper divides into two parts. The main result of the first part is a complete equivariant classification of such actions in terms of the weighted quotient space and a lifting obstruction, when the principal isotropy is the identity, and the action is smooth. In the second part, the author considers the problem of topological classification of 8-manifolds admitting an \(S^3\times S^3\) action, and establishes the stage for the study of the topology of \(\text{Spin}(4)\)-manifolds that accept an \(S^3\times S^3\) action. The work of this paper is an extension and a generalization of the work of \textit{P. Orlik} and \textit{F. Raymond} [Trans. Am. Math. Soc. 152, 531-559 (1970; Zbl 0216.20202); Topology 13, 89-112 (1974; Zbl 0287.57017)].