Cup products, lower central series, and holonomy Lie algebras

Alexander I. Suciu; He Wang

doi:10.1016/j.jpaa.2018.11.006

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arXiv · 1701.07768

Cup products, lower central series, and holonomy Lie algebras

Alexander I. Suciu·He Wang

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Abstract

We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra from finitely presented, commutator-relators groups to arbitrary finitely presented groups. In the process, we give an explicit formula for the cup-product in the cohomology of a finite 2-complex, and an algorithm for computing the corresponding holonomy Lie algebra, using a Magnus expansion method. We illustrate our approach with examples drawn from a variety of group-theoretic and topological contexts, such as link groups, one-relator groups, and fundamental groups of orientable Seifert fibered manifolds.

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Alexander I. Suciu, He Wang. 2017-01-26. Cup products, lower central series, and holonomy Lie algebras. https://doi.org/10.1016/j.jpaa.2018.11.006

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