Generalized Jiang and Gottlieb groups

Abstract

Given a map f: X → Y we extend Gottlieb's result to the generalized Gottlieb group G (Y,f(x 0)and show that the canonical isomorphism π 1(Y, f(x 0)) → (Y) π1(Y,f(x0))→D(Y) restricts to an isomorphism Gf (Y, f(x 0))→ f ∼ 0(Y) Gf(Y,f(x0)) toDf0(Y), where f ∼ 0 (Y) Df 0(Y)is some subset of the group(Y)D(Y) of deck transformations of Y for a fixed lifting f0 of f with respect to universal coverings of X and Y, respectively.