The Lusternik-Schniremann-category and the fundamental group

Abstract

We prove that $$ \cat X\le cd(π_1(X))+\bigg\lceil\frac{\dim X-1}{2}\bigg\rceil$$ for every CW complex $X$ where $cd({\pi }_1(X))$ denotes the cohomological dimension of the fundamental group of $X$.

References in corpus (1)

• Small values of Lusternik-Schnirelmann and systolic categories for manifolds