Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist

Matthew Stoffregen; Michael Willis

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arXiv · 2402.10332

Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist

Matthew Stoffregen·Michael Willis

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Abstract

We construct and study a lift of Jones-Wenzl projectors to the setting of Khovanov spectra, and provide a realization of such lifted projectors via a Cooper-Krushkal-like sequence of maps. We also give a polynomial action on the 3-strand spectral projector allowing a complete computation of the 3-colored Khovanov spectrum of the unknot, proving a conjecture of Lobb-Orson-Sch\"{u}tz. As a byproduct, we disprove a conjecture of Lawson-Lipshitz-Sarkar on the topological Hochschild homology of tangle spectra.

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Matthew Stoffregen, Michael Willis. 2024-02-15. Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist. https://arxiv.org/abs/2402.10332

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