Homology and derived series of groups

Abstract

In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a torsion-free-solvable completion of a group that is analogous to the Malcev completion, with the role of the lower central series replaced by the derived series. We prove that the torsion-free-solvable completion is invariant under rational homology equivalence.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper49.abs.html

References in corpus (4)

• Homology Cobordism Invariants and the Cochran-Orr-Teichner Filtration of the Link Concordance Group
• Chen Lie algebras
• Noncommutative knot theory
• Topology of 3-manifolds and a class of groups II

Cited by in corpus (11)

• Homology Cobordism Invariants and the Cochran-Orr-Teichner Filtration of the Link Concordance Group
• Primary decomposition and the fractal nature of knot concordance
• Monotonicity of Degrees of Generalized Alexander Polynomials of Groups and 3-Manifolds
• The topology on the space of left orderings of a group
• Homology and Derived Series of Groups II: Dwyer's Theorem
• Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders
• Hidden torsion, 3-manifolds, and homology cobordism
• Lower central series and split extensions
• Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
• Homological stability of series of groups
• Alexander invariants and cohomology jump loci in group extensions