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arXiv · 2310.05361

Cohomology on the centric orbit category of a fusion system

George Glauberman·Justin Lynd
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Abstract

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.

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George Glauberman, Justin Lynd. 2023-10-09. Cohomology on the centric orbit category of a fusion system. https://arxiv.org/abs/2310.05361

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