Uniquely compatible transfer systems for cyclic groups of order $p^rq^s$
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913357980762112 |
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| author | Mazur, Kristen Osorno, Angelica M. Roitzheim, Constanze Santhanam, Rekha Van Niel, Danika Castro, Valentina Zapata |
| author_facet | Mazur, Kristen Osorno, Angelica M. Roitzheim, Constanze Santhanam, Rekha Van Niel, Danika Castro, Valentina Zapata |
| contents | Bi-incomplete Tambara functors over a group $G$ can be understood in terms of compatible pairs of $G$-transfer systems. In the case of $G = C_{p^n}$ , Hill, Meng and Li gave a necessary and sufficient condition for compatibility and computed the exact number of compatible pairs. In this article, we study compatible pairs of $G$-transfer systems for the case $G = C_{p^rq^s}$ and identify conditions when such transfer systems are uniquely compatible in the sense that they only form trivially compatible pairs. This gives us new insight into collections of norm maps that are relevant in equivariant homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniquely compatible transfer systems for cyclic groups of order $p^rq^s$ Mazur, Kristen Osorno, Angelica M. Roitzheim, Constanze Santhanam, Rekha Van Niel, Danika Castro, Valentina Zapata Algebraic Topology Combinatorics 55P91, 55N91, 06A07, Bi-incomplete Tambara functors over a group $G$ can be understood in terms of compatible pairs of $G$-transfer systems. In the case of $G = C_{p^n}$ , Hill, Meng and Li gave a necessary and sufficient condition for compatibility and computed the exact number of compatible pairs. In this article, we study compatible pairs of $G$-transfer systems for the case $G = C_{p^rq^s}$ and identify conditions when such transfer systems are uniquely compatible in the sense that they only form trivially compatible pairs. This gives us new insight into collections of norm maps that are relevant in equivariant homotopy theory. |
| title | Uniquely compatible transfer systems for cyclic groups of order $p^rq^s$ |
| topic | Algebraic Topology Combinatorics 55P91, 55N91, 06A07, |
| url | https://arxiv.org/abs/2401.13523 |