The Khovanov homology of infinite braids

Gabriel Islambouli; Michael Willis

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arXiv · 1610.04582

The Khovanov homology of infinite braids

Gabriel Islambouli·Michael Willis

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Abstract

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Khovanov homotopy types of the closures of such braids. Extensions to more general infinite braids are also considered.

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Gabriel Islambouli, Michael Willis. 2016-10-14. The Khovanov homology of infinite braids. https://arxiv.org/abs/1610.04582

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