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Register a new userA generalization of Rasmussens invariant, with applications to surfaces in some four-manifolds
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We extend the definition of Khovanov-Lee homology to links in connected sums of $S^1 times S^2$s, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in $S^1 times S^2$, we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussen-type invariant to the genus of surfaces with boundary in the following four-manifolds: $B^2 times S^2$, $S^1 times B^3$, $mathbb{CP}^2$, and various connected sums and boundary sums of these. We deduce that Rasmussens invariant also gives genus bounds for surfaces inside homotopy 4-balls obtained from $B^4$ by Gluck twists. Therefore, it cannot be used to prove that such homotopy 4-balls are non-standard.
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