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On the mod $p$ cohomology of $BPU(p)$

Author(s): Ales Vavpetic; Antonio Viruel
Journal: Trans. Amer. Math. Soc. 357 (2005), 4517-4532.
MSC (2000): Primary 55R35, 55R15
Posted: June 10, 2005
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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:

Ales Vavpetic
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, Geometr{í}a y Topolog{í}a, Universidad de Málaga, Apdo correos 59, E29080 Málaga, Spain
Email: viruel@agt.cie.uma.es

DOI: 10.1090/S0002-9947-05-03983-8
PII: S 0002-9947(05)03983-8
Received by editor(s): December 4, 2003
Posted: 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 Andaluc{í}a Grant FQM-0213.
Copyright of article: Copyright 2005, American Mathematical Society

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