Morse-Bott functions on manifolds with semi-free circle action

Abstract

Let W²ⁿ be a closed manifold of dimension ≥ 6 with semi-free circle having finitely many fixed points. We study S¹-invariant Morse-Bott functions on W²ⁿ. The aim of this paper is to obtain exact values of minimal numbers of singular circles of some indexes of S¹-invariant Morse-Bott functions on W²ⁿ.