Transfers generate the equivariant stable homotopy category
B. Schäffer, in his thesis, essentially showed that the category of topological spaces and maps, in which Dold's fixed point transfers are added as morphisms, becomes equivalent to the stable homotopy category. In this work, the author establishes the analogous result for a suitable category of \(G\)-spaces, where \(G\) is a compact Lie group. This means that any stable map \(\alpha: X\to Y\) which is \(G\)-equivariant must factor as \(\varphi \circ \tau\) where \(\varphi\) comes from a continuous \(G\)- invariant map and \(\tau\) is a transfer arising from some \(G\)-fixed point situation.
scientific article; zbMATH DE number 612398