Equivariant weak \(n\)-equivalences
This paper starts by giving a good account of the nonequivariant case together with a list of equivalent conditions for weak \(n\)-equivalences constructed by using homology with local coefficients. The main theorem in this paper provides a list of equivalent conditions for a map \(f:X\rightarrow Y\) between path connected CW-spaces to be a \(G\)-equivariant \(n\) equivalence where \(G\) is a discrete group and the fixed point spaces \(X^H\) and \(Y^H\) are path connected CW-spaces and satisfy that the groups \(\pi_1(X^H)\) and \(\pi_1(Y^H)\) are complete and the groups \(\Gamma_\pi\pi_k(Y^H,X^H)\) and \(\Gamma_\pi\pi_k(X^H)\) are trivial for \(k=2,\ldots,n\) and for every group \(H\subseteq G\).
scientific article; zbMATH DE number 1260646