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G&T Monographs |
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Homology and derived series of groups
Tim D Cochran and Shelly L Harvey
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Geometry & Topology 9 (2005)
2159–2191
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Abstract
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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.
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Keywords
derived series, group homology, Malcev
completion, homological localization
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Mathematical Subject Classification
Primary: 20J06
Secondary: 55P60, 57M07
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Publication
Received: 27 January 2005
Revised: 11 November 2005
Accepted: 16 October 2005
Published: 22 November 2005
Proposed: Robion Kirby
Seconded: Cameron Gordon, Joan Birman
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