Volume 11 (2007)

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Modular invariants detecting the cohomology of BF4 at the prime 3

Carles Broto

Geometry & Topology Monographs 11 (2007) 1–16

DOI: 10.2140/gtm.2007.11.1

arXiv: 0903.4865

Abstract

Attributed to J F Adams is the conjecture that, at odd primes, the mod–p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p–subgroups. In this note we rely on Toda's calculation of H*(BF4;F3) in order to show that the conjecture holds in case of the exceptional Lie group F4. To this aim we use invariant theory in order to identify parts of H*(BF4;F3) with invariant subrings in the cohomology of elementary abelian 3–subgroups of F4. These subgroups themselves are identified via the Steenrod algebra action on H*(BF4;F3).

Keywords

classifying space, compact Lie group, cohomology

Mathematical Subject Classification

Primary: 55R40

Secondary: 13A50, 55S10

References
Publication

Received: 22 April 2005
Accepted: 4 October 2005
Published: 14 November 2007

Authors
Carles Broto
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra
Spain