Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Concordance of Bing Doubles and Boundary Genus

CHARLES LIVINGSTONa1 and CORNELIA A. VAN COTTa2

a1 Department of Mathematics, Indiana University, Bloomington, IN, 47405, U.S.A. e-mail: livingst@indiana.edu

a2 Department of Mathematics, University of San Francisco, San Francisco, CA, 94117, U.S.A. e-mail: cvancott@usfca.edu

Abstract

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature σ, then the n–iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than 2n−1σ. The same result holds with σ replaced by 2τ, twice the Ozsváth–Szabó knot concordance invariant.

(Received October 11 2010)

(Online publication July 18 2011)

Footnotes

† Partially supported by NSF-DMS-0707078 and NSF-DMS-1007196.