Rational L-S category and a conjecture of Ganea
To approximate the rational category of a space, \(cat_ 0(S)\), Halperin and Lemaire have introduced an algebraic approximation Mcat(S). In her thesis, K. Hess has shown that \(cat_ 0(S)=Mcat(S)\). The author proves the Ganea's conjecture for Mcat: \(Mcat(T\times S^ k)=Mcat(T)+1\) for all finite 1-connected complexes T and \(k\geq 1\). This implies Ganea's conjecture for \(cat_ 0\). The author gives also lower bounds for cat(E), in a fibration \(F\to E\to B\), in terms of cat B and cohomological information on F.
scientific article; zbMATH DE number 4149148
scientific article