On the Rank of Maps Induced by Fibrations in Homotopy and Homology - Chouingou, Saloua; Zaim, Abdelhadi (Topology Proceedings, 2023)
Let F → E P B be a fibration of simply connected elliptic CW-complexes. Denote Im π_*(p) Q by _i Im{π_i(p) Q: π_i(E) Q → π_i(B) Q} and Im H_*(p ; Q) by _i Im{H_i(p ; Q): H_i(E ; Q) → H_i(B ; Q)} . The topological aspect of this paper is centered around answering the question Is rank π_*(p) Q ≤ rank H_*(p ; Q) ? We are able to prove that, in general, the response must be negative, but in this paper, we will prove the positive in certain reasonable cases.