Alternative stable homotopy classification of

• Autores: Kári Ragnarsson
• Localización: Topology, ISSN 0040-9383, Vol. 45, Nº 3, 2006, págs. 601-610
• Idioma: inglés
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• Resumen

  • We give an alternative to the stable classification of p-completed homotopy types of classifying spaces of finite groups offered by Martino¿Priddy. For a finite group G with Sylow subgroup S, we regard the stable p-completed classifying space as an object under S8BS via the canonical inclusion map. Thus we get a classification in terms of induced fusion systems. Applying Oliver's solution to the Martino¿Priddy conjecture, we obtain the surprising result that the unstable homotopy type of is determined by the map , but not by the homotopy type of .