Characters and transfer maps via categorified traces
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918044536668160 |
|---|---|
| author | Carmeli, Shachar Cnossen, Bastiaan Ramzi, Maxime Yanovski, Lior |
| author_facet | Carmeli, Shachar Cnossen, Bastiaan Ramzi, Maxime Yanovski, Lior |
| contents | We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is that we utilize the interaction between traces and their categorifications. We apply this theory to reprove and refine various results on the composability of Becker-Gottlieb transfers, the Hochschild homology of Thom spectra, and the additivity of traces in stable $\infty$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17364 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characters and transfer maps via categorified traces Carmeli, Shachar Cnossen, Bastiaan Ramzi, Maxime Yanovski, Lior Algebraic Topology Category Theory K-Theory and Homology We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is that we utilize the interaction between traces and their categorifications. We apply this theory to reprove and refine various results on the composability of Becker-Gottlieb transfers, the Hochschild homology of Thom spectra, and the additivity of traces in stable $\infty$-categories. |
| title | Characters and transfer maps via categorified traces |
| topic | Algebraic Topology Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2210.17364 |