Generalizations of Loday's assembly maps for Lawvere's algebraic theories
| Autor: | Bohmann, Anna Marie, Szymik, Markus |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J. Inst. Math. Jussieu 23 (2024) 811--837 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S1474748022000603 |
| Popis: | Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that places both ingredients on the same footing. Building on Elmendorf--Mandell's multiplicativity results and our earlier work, we show that the K-theory of Lawvere theories is lax monoidal. This result makes it possible to present our theory in a user-friendly way without using higher categorical language. It also allows us to extend the idea to new contexts and set up a non-abelian interpolation scheme, raising novel questions. Numerous examples illustrate the scope of our extension. Comment: 24 pages. This paper overlaps with the first version of arXiv:2011.11755, which we have split into two separate papers in order to highlight the two separate directions of results. The current work contains the results on assembly maps and arXiv:2011.11755 focuses on Morita equivalence results. Revised version; to appear in J. Inst. Math. Jussieu |
| Databáze: | arXiv |
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