Skein lasagna modules and handle decompositions

Ciprian Manolescu; Kevin Walker; Paul Wedrich

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arXiv · 2206.04616

Skein lasagna modules and handle decompositions

Ciprian Manolescu·Kevin Walker·Paul Wedrich

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Abstract

The skein lasagna module is an extension of Khovanov-Rozansky homology to the setting of a four-manifold and a link in its boundary. This invariant plays the role of the Hilbert space of an associated fully extended (4+epsilon)-dimensional TQFT. We give a general procedure for expressing the skein lasagna module in terms of a handle decomposition for the four-manifold. We use this to calculate a few examples, and show that the skein lasagna module can sometimes be locally infinite dimensional.

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Ciprian Manolescu, Kevin Walker, Paul Wedrich. 2022-06-09. Skein lasagna modules and handle decompositions. https://arxiv.org/abs/2206.04616

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