## The Lusternik-Schniremann-category and the fundamental group

##### Authors
Dranishnikov, Alexander
##### Description
We prove that $$\cat X\le cd(\pi_1(X))+\bigg\lceil\frac{\dim X-1}{2}\bigg\rceil$$ for every CW complex $X$ where $cd(\pi_1(X))$ denotes the cohomological dimension of the fundamental group of $X$.
##### Keywords
Mathematics - Geometric Topology, 55M30