Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Algebraic and Heegaard–Floer invariants of knots with slice Bing doubles

JAE CHOON CHAa1, CHARLES LIVINGSTONa2 and DANIEL RUBERMANa3

a1 Department of Mathematics Pohang University of Science and Technology (POSTECH) Pohang, Kyungbok 790-784 Republic of Korea. e-mail: jccha@postech.ac.kr

a2 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A. e-mail: livingst@indiana.edu

a3 Department of Mathematics, MS 050, Brandeis University, Waltham, Massachusetts 02454, U.S.A. e-mail: ruberman@brandeis.edu

Abstract

If the Bing double of a knot K is slice, then K is algebraically slice. In addition the Heegaard–Floer concordance invariants τ, developed by Ozsváth–Szabó, and δ, developed by Manolescu and Owens, vanish on K.

(Received February 27 2007)

(Revised April 12 2007)

(Online publication February 11 2008)