\(S^1\)-Bott functions on manifolds (Q362515)

This paper investigates aspects of \(S^1\)-Bott functions on closed manifolds, that is, functions all of whose critical points form nondegenerate critical circles. Standard local structure and topological results on manifolds carrying \(S^1\)-Bott functions are recalled, and the properties of the corresponding diagrams are explored. The authors then study corresponding equivariant notions in manifolds with free or semi-free circle actions.