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Doubly slice knots and metabelian obstructions
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2021-02-06, DOI: 10.1142/s1793525321500229
Patrick Orson, Mark Powell

An n-dimensional knot SnSn+2 is called doubly slice if it occurs as the cross section of some unknotted (n+1)-dimensional knot. For every n it is unknown which knots are doubly slice, and this remains one of the biggest unsolved problems in high-dimensional knot theory. For >1, we use signatures coming from L(2)-cohomology to develop new obstructions for (43)-dimensional knots with metabelian knot groups to be doubly slice. For each >1, we construct an infinite family of knots on which our obstructions are nonzero, but for which double sliceness is not obstructed by any previously known invariant.