Volume 14, issue 4 (2014)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Positive links

Tim D Cochran and Eamonn Tweedy

Algebraic & Geometric Topology 14 (2014) 2259–2298
Abstract

Given a link L S3, we ask whether the components of L bound disjoint, nullhomologous disks properly embedded in a simply connected positive-definite smooth 4–manifold; the knot case has been studied extensively by Cochran, Harvey and Horn. Such a 4–manifold is necessarily homeomorphic to a (punctured) #kP(2). We characterize all links that are slice in a (punctured) #kP(2) in terms of ribbon moves and an operation which we call adding a generalized positive crossing. We find obstructions in the form of the Levine–Tristram signature function, the signs of the first author’s generalized Sato–Levine invariants, and certain Milnor’s invariants. We show that the signs of coefficients of the Conway polynomial obstruct a 2–component link from being slice in a single punctured P(2) and conjecture these are obstructions in general. These results have applications to the question of when a 3–manifold bounds a 4–manifold whose intersection form is that of some #kP(2). For example, we show that any homology 3–sphere is cobordant, via a smooth positive-definite manifold, to a connected sum of surgeries on knots in S3.

Keywords
concordance, slice link, $4$–manifold
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27, 57N70
References
Publication
Received: 12 April 2013
Revised: 12 December 2013
Accepted: 8 January 2014
Published: 28 August 2014
Authors
Tim D Cochran
Department of Mathematics MS-136
Rice University
PO Box 1892
Houston, TX 77251-1892
USA
Eamonn Tweedy
Department of Mathematics MS-136
Rice University
PO Box 1892
Houston, TX 77251-1892
USA