Geometry & Topology 9 (2005) 2129–2158

DOI: 10.2140/gt.2005.9.2129

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 Z). 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 Z semi-direct product Z[1/2]. These two fundamental groups are known to be the only solvable ribbon groups. Our homological condition implies that the Alexander polynomial equals (t-2)(t^-1-2) but also contains information about the metabelian cover of the knot complement (since there are many non-slice knots with this Alexander polynomial).

Note

Example 1.5 is incorrect, for a correct example see the Erratum.

Keywords

slice knots, surgery, Blanchfield pairing

Mathematical Subject Classification

Primary: 57M25

Secondary: 57M27, 57N70

References

Publication

Received: 12 May 2005
Accepted: 10 October 2005
Published: 4 November 2005
Proposed: Robion Kirby
Seconded: Cameron Gordon, Wolfgang Lueck

Authors