Volume 10, issue 2 (2010)

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

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Derivatives of knots and second-order signatures

Tim D Cochran, Shelly Harvey and Constance Leidy

Algebraic & Geometric Topology 10 (2010) 739–787
Abstract

We define a set of “second-order” L(2)–signature invariants for any algebraically slice knot. These obstruct a knot’s being a slice knot and generalize Casson–Gordon invariants, which we consider to be “first-order signatures”. As one application we prove: If K is a genus one slice knot then, on any genus one Seifert surface Σ, there exists a homologically essential simple closed curve J of self-linking zero, which has vanishing zero-th order signature and a vanishing first-order signature. This extends theorems of Cooper and Gilmer. We introduce a geometric notion, that of a derivative of a knot with respect to a metabolizer. We also introduce a new relation, generalizing homology cobordism, called null-bordism.

Keywords
knot concordance, slice knot, $n$–solvable, signature
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M10
References
Publication
Received: 29 December 2008
Revised: 17 January 2010
Accepted: 17 January 2010
Published: 22 March 2010
Authors
Tim D Cochran
Department of Mathematics MS-136
Rice University
PO 1892
Houston, Texas 77251-1892
USA
http://math.rice.edu/~cochran/
Shelly Harvey
Department of Mathematics MS-136
Rice University
PO 1892, Houston, Texas 77251-1892
USA
http://math.rice.edu/~shelly/
Constance Leidy
Department of Mathematics
Wesleyan University
Wesleyan Station
Middletown, CT 06459
USA
http://cleidy.web.wesleyan.edu/