#### Volume 9, issue 4 (2005)

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New topologically slice knots

### Stefan Friedl and Peter Teichner

Geometry & Topology 9 (2005) 2129–2158
 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 $ℤ⋉ℤ\left[1∕2\right]$. These two fundamental groups are known to be the only solvable ribbon groups. Our homological condition implies that the Alexander polynomial equals $\left(t-2\right)\left({t}^{-1}-2\right)$ 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