Characters and transfer maps via categorified traces

Shachar Carmeli; Bastiaan Cnossen; Maxime Ramzi; Lior Yanovski

doi:10.1017/fms.2025.23

Characters and transfer maps via categorified traces

Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi, Lior Yanovski

Weizmann Institute of Science, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a theory of generalized characters of local systems in -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 ∞-categories.

Original language	English
Article number	e93
Journal	Forum of Mathematics, Sigma
Volume	13
DOIs	https://doi.org/10.1017/fms.2025.23
State	Published - 3 Jun 2025

All Science Journal Classification (ASJC) codes

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1017/fms.2025.23License: CC BY

Cite this

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abstract = "We develop a theory of generalized characters of local systems in -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 ∞-categories.",

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AU - Carmeli, Shachar

AU - Cnossen, Bastiaan

AU - Ramzi, Maxime

AU - Yanovski, Lior

PY - 2025/6/3

Y1 - 2025/6/3

N2 - We develop a theory of generalized characters of local systems in -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 ∞-categories.

AB - We develop a theory of generalized characters of local systems in -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 ∞-categories.

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U2 - 10.1017/fms.2025.23

DO - 10.1017/fms.2025.23

M3 - مقالة

SN - 2050-5094

VL - 13

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e93

ER -

Characters and transfer maps via categorified traces

Abstract

All Science Journal Classification (ASJC) codes

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