Vector bundles over classifying spaces of p-local finite groups and Benson–Carlson duality

José Cantarero, Natàlia Castellana, Lola Morales

Research output: Contribution to journalArticleResearch

Abstract

© 2019 London Mathematical Society In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group (S,F,L) in terms of representation rings of subgroups of S. We also prove a stable elements formula for generalized cohomological invariants of p-local finite groups, which is used to show the existence of unitary embeddings of p-local finite groups. Finally, we show that the augmentation C∗(|L|∧p ; Fp) → Fp is Gorenstein in the sense of Dwyer–Greenlees–Iyengar and obtain some consequences about the cohomology ring of |L|∧p.
Original languageEnglish
JournalJournal of the London Mathematical Society
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • 20C20
  • 20D20 (secondary)
  • 55R35 (primary)

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