The Lusternik-Schniremann-category and the fundamental group

Alexander Dranishnikov

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…