Generalized Gottlieb and whitehead center groups of space forms - Golasiński, Marek; de Melo, Thiago [UNESP] (International Press of Boston, 2019)
We extend Oprea's result that the Gottlieb group G1(S2n+1/H) is ZH (the center of H) and show that for a map f: A → S2n+1/H, under some conditions on A, we have G1 f (S2n+1/H) = ZHf*(π1(A)), the centralizer of the image f*(π1(A)) in H. Then, we compute or estimate the groups Gm f (S2n+1/H) and Pm f (S2n+1/H) for certain m > 1.
Keywords: Classifying space; Gottlieb group; Homology group; Homotopy group; Moore- Postnikov tower; N-equivalence; Projective space; Space form; Whitehead center group; Whitehead product