Higher limits over the fusion orbit category

buir.contributor.authorYalçın, Ergün
buir.contributor.orcidYalçın, Ergün|0000-0001-8799-5490
dc.citation.epage69en_US
dc.citation.spage1en_US
dc.citation.volumeNumber406en_US
dc.contributor.authorYalçın, Ergün
dc.date.accessioned2023-02-17T08:50:54Z
dc.date.available2023-02-17T08:50:54Z
dc.date.issued2022-06-09
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractThe fusion orbit category F‾C(G) of a discrete group G over a collection C is the category whose objects are the subgroups H in C, and whose morphisms H→K are given by the G-maps G/H→G/K modulo the action of the centralizer group CG(H). We show that the higher limits over F‾C(G) can be computed using the hypercohomology spectral sequences coming from the Dwyer G-spaces for centralizer and normalizer decompositions for G. If G is the discrete group realizing a saturated fusion system F, then these hypercohomology spectral sequences give two spectral sequences that converge to the cohomology of the centric orbit category Oc(F). This allows us to apply our results to the sharpness problem for the subgroup decomposition of a p-local finite group. We prove that the subgroup decomposition for every p-local finite group is sharp (over F-centric subgroups) if it is sharp for every p-local finite group with nontrivial center. We also show that for every p-local finite group (S,F,L), the subgroup decomposition is sharp if and only if the normalizer decomposition is sharp.en_US
dc.identifier.doi10.1016/j.aim.2022.108482en_US
dc.identifier.eissn1090-2082
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/11693/111483
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.aim.2022.108482en_US
dc.source.titleAdvances in Mathematicsen_US
dc.subjectFusion systemsen_US
dc.subjectHigher limitsen_US
dc.subjectOrbit categoryen_US
dc.subjectp-local finite groupen_US
dc.subjectCohomology of small categoriesen_US
dc.titleHigher limits over the fusion orbit categoryen_US
dc.typeArticleen_US
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