On Ratios of Homotopy and Homology Ranks of Fibrations - Yamaguchi, Toshihiro; Yokura, Shoji (Topology Proceedings, 2020)
For a simply connected CW complex X, we let h(X)= ( π_*(X) Q )H_*(X; Q). In this paper, we propose to evaluate h(X) of the total space X of a fibration ξ: F X → B of elliptic spaces by h(F), h(B), and h(F × B). A conjectural formula is 12 · h(F × B) h(X) < h(F) + h(B) + 14 .