The Ozsváth-Szabó and Rasmussen concordance invariants are not equal

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In this paper we present several counterexamples to Rasmussen's conjecture that the concordance invariant coming from Khovanov homology is equal to twice the invariant coming from Ozsváth-Szabó Floer homology. The counterexamples are twisted Whitehead doubles of the (2,2n+1) torus knots.