# nLab Chevalley fundamental group

The term Chevalley fundamental group is sometimes used for the fundamental group of a space defined via the automorphisms of a universal cover.

This terminology is used by Borceux and Janeldize in their book on Galois Theories. To quote from that source:

” There are two classical definitions of the fundamental group of a topological space which give isomorphic groups for certain ”good” spaces.”

The Chevalley fundamental group $\mathrm{Aut}\left(p\right)=\mathrm{Aut}\left(E,p\right)$ is defined only for connected spaces $B$ which admit a universal covering map $p:E\to B$ with connected $E$, and, of course, depends on it, but again, different $p$ produce isomorphic groups.”

The term algebraic fundamental group is also sometimes used for this, although more usually that term is reserved for Grothendieck’s fundamental group of a scheme.

## References

Revised on September 19, 2012 09:51:55 by Tim Porter (95.147.237.62)