%0 Journal Article %1 suciu2017holonomy %A Suciu, Alexander I. %A Wang, He. %D 2019 %J Journal of Pure and Applied Algebra %K alex myown %N 8 %P 3359-3385 %R https://doi.org/10.1016/j.jpaa.2018.11.006 %T Cup products, lower central series, and holonomy Lie algebras %U https://arxiv.org/abs/1701.07768 %V 223 %X We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra of a group, from finitely presented, commutator-relators groups to arbitrary finitely presented groups. Using the notion of “echelon presentation,” we give an explicit formula for the cup-product in the cohomology of a finite 2-complex. This yields an algorithm for computing the corresponding holonomy Lie algebra, based on a Magnus expansion method. As an application, we discuss issues of graded-formality, filtered-formality, 1-formality, and mildness. 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.

@article{suciu2017holonomy, abstract = {We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra of a group, from finitely presented, commutator-relators groups to arbitrary finitely presented groups. Using the notion of “echelon presentation,” we give an explicit formula for the cup-product in the cohomology of a finite 2-complex. This yields an algorithm for computing the corresponding holonomy Lie algebra, based on a Magnus expansion method. As an application, we discuss issues of graded-formality, filtered-formality, 1-formality, and mildness. 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.}, added-at = {2017-01-27T02:18:18.000+0100}, author = {Suciu, Alexander I. and Wang, He.}, biburl = {https://www.bibsonomy.org/bibtex/2b17c32af8d324d7b5ef7afd2482acea4/asuciu}, description = {Cup products, lower central series, and holonomy Lie algebras}, doi = {https://doi.org/10.1016/j.jpaa.2018.11.006}, interhash = {ea0243af763a8f05a701cb2588246fb5}, intrahash = {b17c32af8d324d7b5ef7afd2482acea4}, journal = {Journal of Pure and Applied Algebra}, keywords = {alex myown}, month = aug, number = 8, pages = {3359-3385}, timestamp = {2019-03-04T20:34:17.000+0100}, title = {Cup products, lower central series, and holonomy Lie algebras}, url = {https://arxiv.org/abs/1701.07768}, volume = 223, year = 2019 }