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Concordance of Bing Doubles and Boundary Genus†

Published online by Cambridge University Press:  18 July 2011

CHARLES LIVINGSTON  and
CORNELIA A. VAN COTT
CHARLES LIVINGSTON
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN, 47405, U.S.A. e-mail: livingst@indiana.edu
CORNELIA A. VAN COTT
Affiliation:
Department of Mathematics, University of San Francisco, San Francisco, CA, 94117, U.S.A. e-mail: cvancott@usfca.edu
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 3 , November 2011 , pp. 459 - 470
Copyright
Copyright © Cambridge Philosophical Society 2011

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