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
and
Department of Mathematics, University of California
Berkeley, CA 94720, USA
Email: friedl@rice.edu, teichner@math.berkeley.edu
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