Equivariant strong shape (Q886292)

Let \(G\) be a compact group. The authors construct the equivariant strong shape category for compact metrizable \(G\)-spaces. They show that if \(f:X\to Y\) is a strong shape equivalence of compact metrizable \(G\)-spaces, then the induced map \(f/G:X/G\to Y/G\) is a strong shape equivalence of the orbit spaces.