ON CATEGORY WEIGHT AND ITS APPLICATIONS

We develop and apply the concept of category weight which was introduced by Fadell and Husseini. For example, we prove that category weight of every Massey product 〈u1, …, un〉, ui∈H̃∗(X) is at least 2 provided X is connected. Furthermore, we remark that elements of maximal category weight enable us to control the Lusternik–Schnirelmann category of a space. For example, we prove that if f: N→M is a map of degree 1 of closed stable parallelizable manifolds and dim M⩽2cat M−4 then cat N⩾cat M. We also prove that if M is a closed manifold with dim M⩽2cat M−3 then cat (M×Sm1×⋯×Smn)=cat M+n, i.e., the Ganea conjecture holds for M.