Mod-two cohomology rings of alternating groups
| Autor: | Dev Sinha, Chad Giusti |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Ring (mathematics) Steenrod algebra Applied Mathematics General Mathematics K-Theory and Homology (math.KT) Mathematics - Rings and Algebras Mathematics::Algebraic Topology Cohomology Transfer (group theory) Nilpotent Rings and Algebras (math.RA) Mathematics::K-Theory and Homology Symmetric group Mathematics - K-Theory and Homology FOS: Mathematics Algebraic Topology (math.AT) Component (group theory) Mathematics - Algebraic Topology Abelian group Mathematics |
| Zdroj: | Journal für die reine und angewandte Mathematik (Crelles Journal). 2021:1-51 |
| ISSN: | 1435-5345 0075-4102 |
| DOI: | 10.1515/crelle-2020-0016 |
| Popis: | We calculate the mod-two cohomology of all alternating groups together, with both cup and transfer product structures, which in particular determines the additive structure and ring structure of the cohomology of individual groups. We show that there are no nilpotent elements in the cohomology rings of individual alternating groups. We calculate the action of the Steenrod algebra and discuss individual component rings. A range of techniques is needed: an almost Hopf ring structure associated to the embeddings of products of alternating groups, the Gysin sequence relating the cohomology of alternating groups to that of symmetric groups, Fox-Neuwirth resolutions, and restriction to elementary abelian subgroups. Comment: 41 pages, 4 figures; v2: minor additions and updates; v3: new figures, substantial revisions to exposition |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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