Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909687526457344 |
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| author | Mehrle, David Quigley, J. D. Stahlhauer, Michael |
| author_facet | Mehrle, David Quigley, J. D. Stahlhauer, Michael |
| contents | We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish above degree one, we present examples where Tor is nonvanishing in almost every degree. We also discuss a 2-primary analogue of the odd-primary Koszul complexes defined in our other work \cite{MQS24a}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups Mehrle, David Quigley, J. D. Stahlhauer, Michael Algebraic Topology We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish above degree one, we present examples where Tor is nonvanishing in almost every degree. We also discuss a 2-primary analogue of the odd-primary Koszul complexes defined in our other work \cite{MQS24a}. |
| title | Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2410.11974 |