Volume 9, issue 4 (2005)

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

Volume 20
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
New topologically slice knots

Stefan Friedl and Peter Teichner

Geometry & Topology 9 (2005) 2129–2158

Erratum: Geometry & Topology 10 (2006) 2501–2504

arXiv: math.GT/0505233

Abstract

In the early 1980’s Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group ). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficient homological condition under which a knot is slice with fundamental group [12]. These two fundamental groups are known to be the only solvable ribbon groups. Our homological condition implies that the Alexander polynomial equals (t 2)(t1 2) but also contains information about the metabelian cover of the knot complement (since there are many non-slice knots with this Alexander polynomial).

Keywords
slice knots, surgery, Blanchfield pairing
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 57N70
References
Forward citations
Publication
Received: 12 May 2005
Accepted: 10 October 2005
Published: 4 November 2005
Proposed: Robion Kirby
Seconded: Cameron Gordon, Wolfgang Lueck
Authors
Stefan Friedl
Department of Mathematics
Rice University
Houston
Texas 77005
USA
Peter Teichner
Department of Mathematics
University of California
Berkeley
California 94720
USA