Cup products, lower central series, and holonomy Lie algebras

DOI10.1016/j.jpaa.2018.11.006OpenAlexW2585798283WikidataQ115345375 ScholiaQ115345375MaRDI QIDQ1739172

He Wang, Alexander I. Suciu

Publication date: 25 April 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07768

zbMATH Keywords

Magnus expansionone-relator grouplower central serieslink groupcohomology ringholonomy Lie algebra

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Graded Lie (super)algebras (17B70) Fundamental group, presentations, free differential calculus (57M05) Derived series, central series, and generalizations for groups (20F14) Associated Lie structures for groups (20F40)

Related Items

Formality and finiteness in rational homotopy theory ⋮ Homology, lower central series, and hyperplane arrangements ⋮ Taylor expansions of groups and filtered-formality ⋮ Formality properties of finitely generated groups and Lie algebras ⋮ Chen ranks and resonance varieties of the upper McCool groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite-type invariants of w-knotted objects. I: \(w\)-knots and the Alexander polynomial
• Jump loci in the equivariant spectral sequence
• Vanishing resonance and representations of Lie algebras
• On a conjecture of K. Murasugi
• Iterated integrals, intersection theory and link groups
• Inert sets and the Lie algebra associated to a group
• Linking numbers and Chen groups
• Homotopy Lie algebras and fundamental groups via deformation theory
• On the intersection ring of compact three manifolds
• Homology, Massey products and maps between groups
• Cohomologically generic 2-complexes and 3-dimensional Poincaré complexes
• The pure braid groups and their relatives
• Homotopy types of complements of 2-arrangements in \(\mathbb{R}^4\)
• Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring
• The pure virtual braid group is quadratic.
• Formality properties of finitely generated groups and Lie algebras
• Chen ranks and resonance varieties of the upper McCool groups
• Graded Lie algebras of type FP
• Topology and geometry of cohomology jump loci
• Pure virtual braids, resonance, and formality
• Homology and central series of groups
• Rational homotopy theory
• On the associated graded ring of a group ring
• On the descending central series of groups with a single defining relation
• Iterated integrals of differential forms and loop space homology
• Integration in free groups
• Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant
• The Lie Algebra Associated to the Lower Central Series of a Link Group and Murasugi's Conjecture
• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Geometric and algebraic aspects of 1-formality
• The Determination of the Lie Algebra Associated to the Lower Central Series of a Group
• Two Exact Sequences in Rational Homotopy Theory Relating Cup Products and Commutators
• Massey Products and Lower Central Series of Free Groups
• On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces
• The Associated Graded Ring of a Group Ring
• The Geometries of 3-Manifolds
• On Milnor's Invariant for Links. II. The Chen Group
• Chen Lie algebras
• Treue Darstellung Liescher Ringe.
• Über Beziehungen zwischen höheren Kommutatoren.
• A Basis for Free Lie Rings and Higher Commutators in Free Groups
• Sur les groupes nilpotents et les anneaux de Lie