Cohomology on the centric orbit category of a fusion system
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909472185647104 |
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| author | Glauberman, George Lynd, Justin |
| author_facet | Glauberman, George Lynd, Justin |
| contents | We study here the higher derived limits of mod $p$ cohomology on the centric orbit category of a saturated fusion system on a finite $p$-group. It is an open problem whether all such higher limits vanish. This is known in many cases, including for fusion systems realized by a finite group and for many classes of fusion systems which are not so realized. We prove that the higher limits of $H^j$ vanish provided $j \leq p-2$, by showing that the same is true for the contravariant part of a simple Mackey composition factor of $H^j$ under the same conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05361 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cohomology on the centric orbit category of a fusion system Glauberman, George Lynd, Justin Group Theory Algebraic Topology 55R35, 20E25 (Primary) 20J06, 20D20, 55R40 (Secondary) We study here the higher derived limits of mod $p$ cohomology on the centric orbit category of a saturated fusion system on a finite $p$-group. It is an open problem whether all such higher limits vanish. This is known in many cases, including for fusion systems realized by a finite group and for many classes of fusion systems which are not so realized. We prove that the higher limits of $H^j$ vanish provided $j \leq p-2$, by showing that the same is true for the contravariant part of a simple Mackey composition factor of $H^j$ under the same conditions. |
| title | Cohomology on the centric orbit category of a fusion system |
| topic | Group Theory Algebraic Topology 55R35, 20E25 (Primary) 20J06, 20D20, 55R40 (Secondary) |
| url | https://arxiv.org/abs/2310.05361 |