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

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 , and for which homotopy sphere the manifold admits a free smooth circle action.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds
