Volume 9, issue 4 (2005)

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Homology and derived series of groups

Tim D Cochran and Shelly L Harvey

Geometry & Topology 9 (2005) 2159–2191

arXiv: math.GT/0407203

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.

Keywords
derived series, group homology, Malcev completion, homological localization
Mathematical Subject Classification 2000
Primary: 20J06
Secondary: 57M07, 55P60
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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
Authors
Tim D Cochran
Department of Mathematics
Rice University
Houston
Texas 77005-1892
USA
Shelly L Harvey
Department of Mathematics
Rice University
Houston
Texas 77005-1892
USA