Quantum topological Hochschild homology and annular Khovanov spectra
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908680202485760 |
|---|---|
| author | Akhmechet, Rostislav Gerhardt, Teena Willis, Michael |
| author_facet | Akhmechet, Rostislav Gerhardt, Teena Willis, Michael |
| contents | Topological Hochschild homology is a topological analogue of classical Hochschild homology of algebras and bimodules. Beliakova, Putyra, and Wehrli introduced quantum Hochschild homology (qHH) and used it to define a quantization of annular Khovanov homology as qHH of the tangle bimodules of Chen-Khovanov and Stroppel. After introducing quantum topological Hochschild homology (qTHH), we construct a new stable homotopy refinement of quantum annular Khovanov homology and show that it agrees with qTHH of the spectral Chen-Khovanov tangle bimodules of Lawson, Lipshitz, and Sarkar. We also show that this new stable homotopy refinement recovers the construction introduced in earlier work of Krushkal together with the first and third authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum topological Hochschild homology and annular Khovanov spectra Akhmechet, Rostislav Gerhardt, Teena Willis, Michael Geometric Topology Algebraic Topology Quantum Algebra 57K18, 55P43 (Primary) 57K16, 55P42 (Secondary) Topological Hochschild homology is a topological analogue of classical Hochschild homology of algebras and bimodules. Beliakova, Putyra, and Wehrli introduced quantum Hochschild homology (qHH) and used it to define a quantization of annular Khovanov homology as qHH of the tangle bimodules of Chen-Khovanov and Stroppel. After introducing quantum topological Hochschild homology (qTHH), we construct a new stable homotopy refinement of quantum annular Khovanov homology and show that it agrees with qTHH of the spectral Chen-Khovanov tangle bimodules of Lawson, Lipshitz, and Sarkar. We also show that this new stable homotopy refinement recovers the construction introduced in earlier work of Krushkal together with the first and third authors. |
| title | Quantum topological Hochschild homology and annular Khovanov spectra |
| topic | Geometric Topology Algebraic Topology Quantum Algebra 57K18, 55P43 (Primary) 57K16, 55P42 (Secondary) |
| url | https://arxiv.org/abs/2511.23441 |