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Characters and transfer maps via categorified traces

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arxiv 2210.17364 v3 pith:YPN7SPL7 submitted 2022-10-31 math.AT math.CTmath.KT

Shachar Carmeli , Bastiaan Cnossen , Maxime Ramzi , Lior Yanovski This is my paper · ORCID
classification math.ATmath.CTmath.KT
keywords theorytracescategoriescharactercharactersinftyadditivityapply
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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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Cited by 1 Pith paper

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  1. On the Farrell--Tate $K$-theory of $\text{Out}(F_n)$

    math.AT 2025-05 accept novelty 7.0 of 10

    For every prime p at least 11, the p-adic Farrell-Tate K-theory of Out(F_{p+1}) has an odd summand of dimension (p-7)(p-5)/24, yielding the first computer-free odd class in K^1(BOut(F_{12})) tensor Q.

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