The rational cohomology of a p-local compact group

C Broto, R Levi, B Oliver

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

For any prime $ p$, the theory of $ p$-local compact groups is modelled on the $ p$-local homotopy theory of classifying spaces of compact Lie groups and $ p$-compact groups and generalises the earlier concept of $ p$-local finite groups. These objects have maximal tori and Weyl groups, although the Weyl groups need not be generated by pseudoreflections. In this paper, we study the rational $ p$-adic cohomology of the classifying space of a $ p$-local compact group and prove that just as for compact Lie groups, it is isomorphic to the ring of invariants of the Weyl group action on the cohomology of the classifying space of the maximal torus. This is applied to show that unstable Adams operations on $ p$-local compact groups are determined in the appropriate sense by the map they induce on rational cohomology.
Original languageEnglish
Pages (from-to)1035-1043
Number of pages9
JournalProceedings of the American Mathematical Society
Volume142
Issue number3
Early online date24 Sep 2013
DOIs
Publication statusPublished - 2014

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Lie groups
Compact Group
Cohomology
Classifying Space
Weyl Group
Compact Lie Group
Torus
P-compact Group
Adams Operations
Homotopy Theory
Group Action
P-adic
Finite Group
Isomorphic
Unstable
Ring
Generalise
Invariant

Cite this

The rational cohomology of a p-local compact group. / Broto, C; Levi, R; Oliver, B.

In: Proceedings of the American Mathematical Society, Vol. 142, No. 3, 2014, p. 1035-1043.

Research output: Contribution to journalArticle

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