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

Published online by Cambridge University Press:  24 October 2008

Tim. D. Cochran
Tim. D. Cochran
Affiliation:
Mathematical Sciences Research Institute, Berkeley, CA 94720, U.S.A.
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 465 - 472
Copyright
Copyright © Cambridge Philosophical Society 1985

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