Morse theory on \(G\)-manifolds (Q697619)

The authors define the Morse polynomial for a \(G\)-equivariant Morse function \(f\) defined on \(M\), where \(G\) is a finite group acting semifreely on the compact manifold \(M\). If \(\text{codim} (M^G)\leq 2\) and if \(f\) is an equivariant Morse function on \(M\) such that \(f|_MG\) is also a Morse function, then they show that the Morse polynomial of \(f\) completely reflects a \(G-CW\) structure of \(M\). These results are directely connected to those obtained by \textit{R. Bott} [Ann. Math. (2) 60, 248-261 (1954; Zbl 0058.09101); Bull. Am. Math. Soc., New Ser. 7, 331-358 (1982; Zbl 0505.58001)] and \textit{A. G. Wasserman} [Topology 8, 127-150 (1969; Zbl 0215.24702)].