The Ozsváth-szabó and Rasmussen concordance invariants are not equal

Abstract

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 (2, 2n + 1) torus knots. © 2008 by The Johns Hopkins University Press.