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arXiv · 2210.17364

Characters and transfer maps via categorified traces

Shachar Carmeli·Bastiaan Cnossen·Maxime Ramzi·Lior Yanovski
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Abstract

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.

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Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi, Lior Yanovski. 2022-10-31. Characters and transfer maps via categorified traces. https://doi.org/10.1017/fms.2025.23

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