Volume 9, issue 4 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
References
Forward citations
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