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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the mod $p$ cohomology of $BPU(p)$
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by Aleš Vavpetič and Antonio Viruel PDF
Trans. Amer. Math. Soc. 357 (2005), 4517-4532 Request permission

Abstract:

We study the mod $p$ cohomology of the classifying space of the projective unitary group $PU(p)$. We first prove that conjectures due to J.F. Adams and Kono and Yagita (1993) about the structure of the mod $p$ cohomology of the classifying space of connected compact Lie groups hold in the case of $PU(p)$. Finally, we prove that the classifying space of the projective unitary group $PU(p)$ is determined by its mod $p$ cohomology as an unstable algebra over the Steenrod algebra for $p>3$, completing previous work by Dwyer, Miller and Wilkerson (1992) and Broto and Viruel (1998) for the cases $p=2,3$.
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Additional Information
  • Aleš Vavpetič
  • Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1111 Ljubljana, Slovenia
  • Email: ales.vavpetic@FMF.Uni-Lj.Si
  • Antonio Viruel
  • Affiliation: Dpto de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, E29080 Málaga, Spain
  • MR Author ID: 630145
  • ORCID: 0000-0002-1605-5845
  • Email: viruel@agt.cie.uma.es
  • Received by editor(s): December 4, 2003
  • Published electronically: June 10, 2005
  • Additional Notes: The first author was partially supported by the Ministry for Education, Science and Sport of the Republic of Slovenia research program No. 0101-509. The second author was partially supported by the DGES-FEDER grant BFM2001-1825, and Junta de Andalucía Grant FQM-0213.
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4517-4532
  • MSC (2000): Primary 55R35, 55R15
  • DOI: https://doi.org/10.1090/S0002-9947-05-03983-8
  • MathSciNet review: 2156719