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Basic Commutators and Minimal Massey Products

Published online by Cambridge University Press:  20 November 2018

Roger Fenn  and
Denis Sjerve
Roger Fenn
Affiliation:
University of Sussex, Sussex, England
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 Massey products defined on two dimensional polyhedra, initiated in [13]. It will be shown that for many such spaces there is a hyperbolic model which can be used to study Massey products. More precisely, Massey products may be interpreted as intersections of geodesies in the Poincaré model. These elements are called minimal Massey products and are the analogue of Massey products over a system considered in Porter's paper. They enjoy the property of being uniquely defined (without indeterminacy) and of being multilinear and natural. Minimal products also satisfy symmetry properties generalising the symmetry properties enjoyed by cup products.

A device which will be useful in the proof of the main theorem, 7.4, is the introduction of a class of complexes called basic complexes. These generalise the notion of a surface and each one houses a standard copy of a Massey product.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 6 , 01 December 1984 , pp. 1119 - 1146
Copyright
Copyright © Canadian Mathematical Society 1984

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