Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913235610894336 |
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| author | Stoffregen, Matthew Willis, Michael |
| author_facet | Stoffregen, Matthew Willis, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist Stoffregen, Matthew Willis, Michael Geometric Topology 57K18 (Primary) 57K10, 55P42 (Secondary) 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. |
| title | Jones-Wenzl projectors and the Khovanov homotopy of the infinite twist |
| topic | Geometric Topology 57K18 (Primary) 57K10, 55P42 (Secondary) |
| url | https://arxiv.org/abs/2402.10332 |