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September 27, 2025Open Access

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

Key Points

The construction yields a realization of Jones–Wenzl projectors within Khovanov spectra, integrating advanced methods.
It completes the computation of the 3-colored Khovanov spectrum of the unknot, confirming the conjecture posed by Lobb–Orson–Schütz.
The approach uses a Cooper–Krushkal-like sequence of maps, facilitating the analysis of projectors in the given context.
This work also disproves a conjecture related to the topological Hochschild homology of tangle spectra, showcasing significant results.

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–Schütz. As a byproduct, we disprove a conjecture of Lawson–Lipshitz–Sarkar on the topological Hochschild homology of tangle spectra.

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Stoffregen et al. (Thu,) studied this question.

synapsesocial.com/papers/68d7be66eebfec0fc5237daf https://doi.org/https://doi.org/10.4171/qt/246

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