The Kronheimer-Mrowka instanton invariant s# is not additive under connected sums and differs from Rasmussen's s, and new link invariants s#_+ and s#_- are constructed and computed for torus links.
Gauge theory and Rasmussen's invariant
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abstract
A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not. In particular, the gauge-theory counterpart of s(K) is not additive for connected sums.
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On the Kronheimer-Mrowka concordance invariant
The Kronheimer-Mrowka instanton invariant s# is not additive under connected sums and differs from Rasmussen's s, and new link invariants s#_+ and s#_- are constructed and computed for torus links.