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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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