Gauge theory and Rasmussen's invariant

By P. Kronheimer, T. Mrowka. 2011

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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 2 g(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 Σ in any homotopy 4‐ball.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a39a7bc3fc9f16cf5d451ac3d9eb55eda67dca44