Free circle actions on certain simply connected $7-$manifolds

TL;DR

This paper classifies when certain 7-manifolds, constructed from products of spheres and a homotopy sphere, admit free smooth circle actions, expanding understanding of symmetry properties in high-dimensional topology.

Contribution

It provides a complete characterization of free circle actions on a class of simply connected 7-manifolds formed by connected sums of sphere products and a homotopy sphere.

Findings

Identifies conditions on integers k, l for free circle actions

Determines which homotopy 7-spheres admit such actions

Advances classification of symmetries in high-dimensional manifolds

Abstract

In this paper, we determine for which nonnegative integers $k$, $l$ and for which homotopy $7-$sphere $\Sigma$ the manifold $kS^{2}\times S^{5}\#lS^{3}\times S^{4}\#\Sigma$ admits a free smooth circle action.