  We obtain new invariants of topological link concordance and homology
cobordism of 3-manifolds from Hirzebruch-type intersection form defects of
towers of iterated p-covers. Our invariants can extract geometric information
from an arbitrary depth of the derived series of the fundamental group, and can
detect torsion which is invisible via signature invariants. Applications
illustrating these features include the following: (1) There are infinitely
many homology equivalent rational 3-spheres which are indistinguishable via
multisignatures, eta-invariants, and L2-signatures but have distinct homology
cobordism types. (2) There is an infinite family of 2-torsion (amphichiral)
knots, including the figure eight knot, with non-slice iterated Bing doubles;
as a special case, we give the first proof of the conjecture that the Bing
double of the figure eight knot is not slice. (3) There exist infinitely many
torsion elements at any depth of the Cochran-Orr-Teichner filtration of link
concordance.
