#### Volume 10, issue 2 (2010)

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The Lusternik–Schnirelmann category and the fundamental group

### Alexander Dranishnikov

Algebraic & Geometric Topology 10 (2010) 917–924
##### Abstract

We prove that

${cat}_{LS}X\le cd\left({\pi }_{1}\left(X\right)\right)+⌈\frac{dimX-1}{2}⌉$

for every CW–complex $X$ where $cd\left({\pi }_{1}\left(X\right)\right)$ denotes the cohomological dimension of the fundamental group of $X$.

##### Keywords
Lusternik–Schnirelmann category, cohomological dimension, fundamental group
Primary: 55M30