The Ozsv{\'a}th-Szab{\'o} and Rasmussen concordance invariants are not equal

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 Ozsv{'a}th-Szab{'o} Floer homology. The counterexamples are twisted Whitehead doubles of the (2,2n+1) torus knots.