Gauge theory and Rasmussen's invariant

Using a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] with boundary K, it is shown in this paper that s[superscript ♯](K) (and therefore s(K)) similarly bounds the genus of such a surface Σ in any homotopy 4-ball.National Science Foundation (U.S.) (Grant DMS-0805841