Equivariant homotopy theory and Milnor’s theorem

Source abstract

The foundations of equivariant homotopy and cellular theory are examined; an equivariant Whitehead theorem is proved, and the classical results by Milnor about spaces with the homotopy-type of a CW complex are generalized to the equivariant case. The ambient group G is assumed compact Lie. Further results include equivariant cellular approximation and the procedure for replacement of an arbitrary G -space by a G -CW complex.