The rational LS-category of k-trivial fibrations

摘要

We provide new upper and lower bounds for the rational LS-category of a rational fibration xi : F --> E --> K(Q; 2n) of simply connected spaces that depend on a measure of the triviality of xi which is strictly finer than the vanishing of the higher holonomy actions. In particular, we prove that if xi is k-trivial for some k greater than or equal to 0 and H*(F) enjoys Poincare duality, then cat(0) E greater than or equal to cat(0) F + k. [References: 16]