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For $\ell >1$, we develop $L^{(2)}$-signature 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 ourobstructions are non-zero, but for which double sliceness is not obstructed byany previously known invariant.

Doubly slice knots and metabelian obstructions