Modular invariants detecting the cohomology of BF_4 at the prime 3

Details Modular invariants detecting the cohomology of BF_4 at the prime 3 Modular invariants detecting the cohomology of BF_4 at the prime 3

2009-03-27

arxiv.org/abs/0903.4865v1

Geom. Topol. Monogr. 11 (2007) 1-16

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 14 November 2007

Scientific paper

10.2140/gtm.2007.11.1

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^*(BF_4;F_3) in order to show that the conjecture holds in case of the exceptional Lie group F_4. To this aim we use invariant theory in order to identify parts of H^*(BF_4;F_3) with invariant subrings in the cohomology of elementary abelian 3-subgroups of F_4. These subgroups themselves are identified via the Steenrod algebra action on H^*(BF_4;F_3).

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