We give a new geometric obstruction to the iterated Bing double of a knot being a slice
link: for
the –st
iterated Bing double of a knot is rationally slice if and only if the
–th iterated
Bing double of the knot is rationally slice. The main technique of the proof is a covering link
construction simplifying a given link. We prove certain similar geometric obstructions for
as well. Our
results are sharp enough to conclude, when combined with algebraic invariants, that if the
–th iterated Bing double
of a knot is slice for some ,
then the knot is algebraically slice. Also our geometric arguments applied to the
smooth case show that the Ozsváth–Szabó and Manolescu–Owens invariants give
obstructions to iterated Bing doubles being slice. These results generalize recent
results of Harvey, Teichner, Cimasoni, Cha and Cha–Livingston–Ruberman.
As another application, we give explicit examples of algebraically slice
knots with nonslice iterated Bing doubles by considering von Neumann
–invariants
and rational knot concordance. Refined versions of such examples are given, that take
into account the Cochran–Orr–Teichner filtration.