Patrick Orson, Mark Powell

An $n$-dimensional knot ${S}^{n}\subset {S}^{n+2}$ 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 $\ell >1$, we use signatures coming from ${L}^{(2)}$-cohomology to develop new obstructions for $(4\ell -3)$-dimensional knots with metabelian knot groups to be doubly slice. For each $\ell >1$, 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.