Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A topological proof of Stallings' theorem on lower central series of groups

Tim. D. Cochrana1

a1 Mathematical Sciences Research Institute, Berkeley, CA 94720, U.S.A.

For a topologist, the fundamental group G of a space is usually the most important non-abelian algebraic object of study. However, under many equivalence relationships G is not invariant, so topologists have been led to examine other algebraic objects. In particular, for questions of concordance the lower central series of G seems to play the crucial role. Recall that the lower central series Gn(n = 1,2,...) of G is defined by G1 = G, Gn = [G, Gn_1] for n > 1, and the lower central sequence of G is the sequence of quotients G/Gn.

(Received June 22 1984)