The Lusternik-Schnirelmann category of certain infinite CW-complexes
The author settles in the negative two questions concerning \(\text{cat}(X)\). First of all the LS-category of a 1-connected finite type CW-complex \(X\) which is the homotopy colimit of a sequence \(X_1\to X_2\to X_3\to\cdots\) of 1-connected finite CW-complexes may exceed the LS-category of each \(X_i\). For instance, the category of the mapping cone \(X\) of an essential phanton map \(f:\sum k(Z,5)\to S^4\) is two and the LS-categories of the skeleta are one. The author also constructs 1-connected finite type CW-complexes \(X\), \(Y\) in the same genus such that \(\text{cat }X= 2\) and \(\text{cat }Y= 1\).
scientific article; zbMATH DE number 1356312