 Title : On Independence of Iterated Whitehead Doubles in the Knot Concordance Group  Speaker : Kyungbae Park (Michigan State University)  Date : 11 a.m. 12(Noon),Friday, 31 May 2013  Place : The GAIA (Math Science building room 106)  Abstract Let D(K) be the positivelyclasped untwisted Whitehead double of a knot K, and T(p, q) be the (p, q) torus knot. We show that D(T(2, 2m+1)) and D(D(T(2, 2m+1))) differ in the smooth concordance group of knots for each m>1. In fact, they generate a Z2 summand in the subgroup generated by topologically slice knots. We use the concordance invariant δ by Manolescu and Owens. More generally, we show that the same result holds for a knot K with δ(D(K))>8 and give a formula to compute δ(D(K)) for some classes of knots. Interestingly, these results are not easily be shown using other concordance invariants such as the knot signature and τinvariants of the knot Floer theory. We also determine the knot Floer complex of D(T(2, 2m+1)) for any m>0 generalizing a result for T(2, 3) of Hedden, Kim and Livingston.
 Contact: Jihye Jung (POSTECH, Tel. 2798020)

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