An upper bound on the LS-category in presence of the fundamental group

Abstract

We prove that $$ \cat X\le \frac{\cd(π_1(X))+\dim X}{2}$$ for every CW complex $X$ where $\cd(π_1(X))$ denotes the cohomological dimension of the fundamental group of $X$. We obtain this as a corollary of the inequality $$ \cat X\le\frac{\cat (u_X)+\dim X}{2} $$ where $u_X:X\to B{\pi }_1(X)$ is a classifying map for the universal covering of $X$.

References in corpus (3)

• On the Berstein-Svarc Theorem in dimension 2
• Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles
• The LS-category of the product of lens spaces