Slicing mixed Bing-Whitehead doubles
arXiv:0912.5222 · doi:10.1112/jtopol/jts019
Abstract
We show that if K is any knot whose Ozsvath-Szabo concordance invariant tau(K) is positive, the all-positive Whitehead double of any iterated Bing double of K is topologically but not smoothly slice. We also show that the all-positive Whitehead double of any iterated Bing double of the Hopf link (e.g., the all-positive Whitehead double of the Borromean rings) is not smoothly slice; it is not known whether these links are topologically slice.
16 pages, 10 figures. v2: This is a substantial revision of v1. We eliminated Section 4 of v1 because it is superceded by arXiv:1008.3349. v3: corrected references