Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$ p$-subgroups of compact Lie groups and torsion of infinite height in $ H\sp{\ast} (BG)$


Author: Mark Feshbach
Journal: Trans. Amer. Math. Soc. 259 (1980), 227-233
MSC: Primary 55R40
DOI: https://doi.org/10.1090/S0002-9947-1980-0561834-8
MathSciNet review: 561834
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The relation between elementary abelian p-subgroups of a connected compact Lie group G and the existence of p-torsion in $ {H^ {\ast} }(G)$ has been known for some time [B-S]. In this paper we prove that if G is any compact Lie group then $ {H^ {\ast} }(BG)$ contains p-torsion of infinite height iff G contains an elementary abelian p-group not contained in a maximal torus. The hard direction is proven using the double coset theorem for the transfer. A third equivalent condition is also given.


References [Enhancements On Off] (What's this?)

  • [B] A. Borel, Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes, Tôhoku Math. J. 13 (1961), 216-240. MR 0147579 (26:5094)
  • [B-S] A. Borel and J. P. Serre, Sur certains sous-groupes des groupes de Lie compacts, Comment. Math. Helv. 27 (1953), 128-139. MR 0054612 (14:948d)
  • [F] M. Feshbach, The transfer and compact Lie groups, Trans. Amer. Math. Soc. 251 (1979), 139-169. MR 531973 (80k:55049)
  • [Q] D. Quillen, The spectrum of an equivariant cohomology ring. I, Ann. of Math. (2) 94 (1971), 549-572. MR 0298694 (45:7743)
  • [S] R. G. Swan, The nontriviality of the restriction map in the cohomology of groups, Proc. Amer. Math. Soc. 11 (1960), 885-887. MR 0124050 (23:A1370)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55R40

Retrieve articles in all journals with MSC: 55R40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0561834-8
Keywords: Double coset formula, elementary abelian p-groups, torsion of infinite height, classifying space, transfer, compact Lie group
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society