LS-category of CW-complexes with 3 cells in R-local homotopy theory (Q1385199)

In this interesting paper the authors study the Lyusternik-Shnirel'man category of some CW-complexes with 3 cells, built on \(Y= S^{2n} \bigcup_{k[i_{2n}, i_{2n}]} e^{4n}\), where \(i_j\) is the identity map of \(S^j\) and \([ ,\;]\) denotes the Whitehead bracket. In particular, the following result is obtained: an \(R\)-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with \(3R\)-cells, has a cup product of length 3 in its cohomology algebra.