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Kirby Belts and the Skein Lasagna Module of $S^2\times S^2$.

Student-Run Research Seminar

Speaker: Ian Sullivan, UC Davis
Location: 3106 Mathematical Science Building
Start time: Wed, Nov 29 2023, 12:10PM

The lasagna module of a chosen link homology theory is a relatively new kind of smooth $4$-manifold invariant. In general, these invariants are difficult to compute, often requiring a colimit of "symmetrized" Khovanov homology groups. In this talk, we define and investigate a certain homotopy colimit of a directed system of Khovanov homology tangle complexes. We then propose a new "local" computation tool for $4$-manifolds whose Kirby diagrams contain certain tangles, and use this technique to compute the $gl_{2}$-Khovanov homology flavored skein lasagna module of some new manifolds, including $S^2\times S^2$. 

Free pizzas:)