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 Aut(p)=Aut(E,p)Aut(p)= Aut(E,p) is defined only for connected spaces BB which admit a universal covering map p:EBp: E\to B with connected EE, and, of course, depends on it, but again, different pp 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.


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