We extend the definition of Khovanov-Lee homology to links in connected sums of S1×S2, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in S1×S2,
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: B2×S2, S1×B3, CP2,
and various connected sums and boundary sums of these. We deduce that
Rasmussen's invariant also gives genus bounds for surfaces inside
homotopy four-balls obtained from B4
by a certain operation called Gluck twists. Therefore, Rasmussen’s
invariant cannot be used to prove that such homotopy four-balls are
non-standard.
This talk was part of the conference "Perspectives on quantum link
homology theories", see https://cbz20.raspberryip.com/Perspectives-2021