Qiuyu Ren (UCB) “(Khovanov) skein lasagna modules of 4-manifolds”

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Abstract: For any well-behaved link homology theory for links in the 3-sphere, Morrison–Walker–Wedrich defined an invariantĀ for smooth 4-manifolds called skein lasagna modules, which can be viewed as an upgrade of the input link homology theory. We review the definition and investigate some formal properties of the invariant. We also introduce a few variations of the invariant. In the case where the input link homology theory is Khovanov homology, the resulting skein lasagna modules are strong enough to detect exotic 4-manifolds, i.e. smooth 4-manifolds that are homeomorphic but not diffeomorphic. This is a sequence of two expository talks, partly based on joint work with I. Sullivan, P. Wedrich, M. Willis, and M. Zhang.