On equivariant fibrations (Q1420750)

Let \(G\) be a compact Lie group. An equivariant map \(p: E\to B\) of \(G\)-spaces that satisfies an appropriate covering homotopy property is an equivariant Hurewicz fibration [see \textit{S. Waner}, Trans. Am. Math. Soc. 258, 369--384 (1980; Zbl 0444.55013) and 385--405 (1980; Zbl 0447.55011)]. Replacing the covering homotopy property by the weaker version due to \textit{A. Dold} [Ann. Math. (2) 78, 223--255 (1963; Zbl 0203.25402)], the authors prove the equivalence of five different definitions of the resulting equivariant Dold fibration. They also prove that a local equivariant Dold fibration is an equivariant Dold fibration.