Volume 12, issue 1 (2008)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group

Shelly L Harvey

Geometry & Topology 12 (2008) 387–430
Abstract

For any group G, we define a new characteristic series related to the derived series, that we call the torsion-free derived series of G. Using this series and the Cheeger–Gromov ρ–invariant, we obtain new real-valued homology cobordism invariants ρn for closed (4k1)–dimensional manifolds. For 3–dimensional manifolds, we show that {ρn|n } is a linearly independent set and for each n 0, the image of ρn is an infinitely generated and dense subset of .

In their seminal work on knot concordance, T Cochran, K Orr and P Teichner define a filtration (n)m of the m–component (string) link concordance group, called the (n)–solvable filtration. They also define a grope filtration Gnm. We show that ρn vanishes for (n+1)–solvable links. Using this, and the nontriviality of ρn, we show that for each m 2, the successive quotients of the (n)–solvable filtration of the link concordance group contain an infinitely generated subgroup. We also establish a similar result for the grope filtration. We remark that for knots (m = 1), the successive quotients of the (n)–solvable filtration are known to be infinite. However, for knots, it is unknown if these quotients have infinite rank when n 3.

Keywords
link concordance, derived series, homology cobordism
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 20F14
References
Publication
Received: 9 April 2007
Revised: 2 September 2007
Accepted: 15 November 2007
Published: 12 March 2008
Proposed: Peter Teichner
Seconded: Peter Ozsvath, Ron Fintushel
Authors
Shelly L Harvey
Department of Mathematics
Rice University
PO Box 1892, MS 136
Houston TX 77005-1892
USA
http://math.rice.edu/~shelly/