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Massey Products and Lower Central Series of Free Groups

Published online by Cambridge University Press:  20 November 2018

Roger Fenn  and
Denis Sjerve
Roger Fenn
Affiliation:
University of British Columbia, Vancouver, British Columbia
Denis Sjerve
Affiliation:
University of British Columbia, Vancouver, British Columbia
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The purpose of this paper is to continue the investigation into the relationships amongst Massey products, lower central series of free groups and the free differential calculus (see [4], [9], [12]). In particular we set forth the notion of a universal Massey product ≪α1, …, αk≫, where the αi are one dimensional cohomology classes. This product is defined with zero indeterminacy, natural and multilinear in its variables.

In order to state the results we need some notation. Throughout F will denote the free group on fixed generators x1, …, xn and

will denote the lower central series of F. If I = (i1, …, ik) is a sequence such that 1 ≦ i1, …, ik ≦ n then ∂1 is the iterated Fox derivative and , where is the augmentation. By convention we set ∂1 = identity if I is empty.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 2 , 01 April 1987 , pp. 322 - 337
Copyright
Copyright © Canadian Mathematical Society 1987

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