Generalizations of Loday's assembly maps for Lawvere's algebraic theories
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866911947190960128 |
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| author | Bohmann, Anna Marie Szymik, Markus |
| author_facet | Bohmann, Anna Marie Szymik, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07003 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalizations of Loday's assembly maps for Lawvere's algebraic theories Bohmann, Anna Marie Szymik, Markus K-Theory and Homology Algebraic Topology 19D23 (Primary), 18F25, 18C10, 55P42 (secondary) 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. |
| title | Generalizations of Loday's assembly maps for Lawvere's algebraic theories |
| topic | K-Theory and Homology Algebraic Topology 19D23 (Primary), 18F25, 18C10, 55P42 (secondary) |
| url | https://arxiv.org/abs/2112.07003 |