Ramified coverings, orbit projections and symmetric powers

Source abstract

L. Smith, in a recent paper [11], studied a class of maps X → Y which he called ramified coverings. Roughly speaking, these are maps with a multiple-valued inverse Y → SP d X ; cf. 1·1. He showed that X → X/G is a ramified covering whenever a finite group G acts on X . Using results of [4] on infinite symmetric powers SP ∞ X of CW -complexes X he obtained transfer homomorphisms .