Algebraic concordance of knots and their Bing doubles

Abstract

We show that a knot is algebraically slice if and only if its Bing double is algebraically boundary slice as a boundary link using an algebraic characterization of algebraic boundary concordance of boundary links. Since Seifert matrix constitutes a complete invariant up to boundary link concordance for higher dimensional knots, a higher dimensional knot is slice if and only if its Bing double is boundary-slice.