The equivariant Hurewicz map

L. Gaunce Lewis
1992 Transactions of the American Mathematical Society  
Let G be a compact Lie group, Y be a based G-space, and V be a G-representation. If Tty(Y) is the equivariant homotopy group of Y in dimension V and Hft(Y) is the equivariant ordinary homology group of Y with Burnside ring coefficients in dimension V , then there is an equivariant Hurewicz map h: 4(Y) ^ H°(Y). One should not expect this map to be an isomorphism, since Hfi(Y) must be a module over the Burnside ring, but it<fi(Y) need not be. However, here it is shown that, under the obvious
more » ... ctivity conditions on Y , this map induces an isomorphism between Hft(Y) and an algebraically defined modification of n$(Y).
doi:10.1090/s0002-9947-1992-1049614-9 fatcat:6yycwew2effklhxom7e7kqostm