LAUSR

Let D(K) be the positively clasped untwisted Whitehead double of a knot K, and Tp,q be the (p,q) torus knot. We show that D(T2,2m+1) and D2(T 2,2m+1) are linearly independent in the smooth knot concordance group ???? for each m ≥ 2. Further, D(T2,5) and D2(T 2,5) generate a ℤ ⊕ ℤ summand in the subgroup of ???? generated by topologically slice knots. We use the concordance invariant δ of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the τ-invariant of knot Floer theory and the s-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of D(T2,2m+1) for any m ≥ 1 generalizing a result for T2,3 of Hedden, Kim and Livingston.