Cup products, lower central series, and holonomy Lie algebras
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.
Keywords
Cite
@article{arxiv.1701.07768,
title = {Cup products, lower central series, and holonomy Lie algebras},
author = {Alexander I. Suciu and He Wang},
journal= {arXiv preprint arXiv:1701.07768},
year = {2019}
}
Comments
27 pages; accepted for publication in the Journal of Pure and Applied Algebra. arXiv admin note: substantial text overlap with arXiv:1504.08294