Geometry & Topology, Vol. 9 (2005) Paper no. 48, pages 2129--2158.

New topologically slice knots

Stefan Friedl, Peter Teichner

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).

Keywords. Slice knots, surgery, Blanchfield pairing

AMS subject classification. Primary: 57M25. Secondary: 57M27, 57N70.

E-print: arXiv:math.GT/0505233

DOI: 10.2140/gt.2005.9.2129

Submitted to GT on 12 May 2005. Paper accepted 10 October 2005. Paper published 4 November 2005.

Notes on file formats

Stefan Friedl, Peter Teichner
Department of Mathematics, Rice University
Houston, TX 77005, US
Department of Mathematics, University of California
Berkeley, CA 94720, USA

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