Journal of the European Mathematical Society


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Volume 12, Issue 3, 2010, pp. 555–610
DOI: 10.4171/JEMS/209

Published online: 2010-04-20

Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers

Jae Choon Cha[1]

(1) Pohang University of Science and Technology, South Korea

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, η-invariants, and L2-signatures but have distinct homology cobordism types. (2) There is an infinite family of 2-torsion (amphichiral) knots 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.

Keywords: Link concordance, homology cobordism, iterated p-cover, intersection form defect, Bing double

Cha Jae Choon: Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers. J. Eur. Math. Soc. 12 (2010), 555-610. doi: 10.4171/JEMS/209