Gauge theory and rasmussen's invariant

Abstract

Using a version of instanton homology, an integer invariant s#(K) is defined for knots K in S3. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2g(σ) for any surface σ in B4 with boundary K, it is shown in this paper that s#(K) (and therefore s(K)) similarly bounds the genus of such a surface ∑ in any homotopy 4-ball. © 2013 London Mathematical Society.