Doubly slice knots and metabelian obstructions

Abstract

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 our obstructions are non-zero, but for which double sliceness is not obstructed by any previously known invariant.

22 pages, 0 figures, comments welcome!