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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On The Homotopy Type of $BG$ for
Certain Finite 2-Groups $G$


Authors: Carlos Broto and Ran Levi
Journal: Trans. Amer. Math. Soc. 349 (1997), 1487-1502
MSC (1991): Primary 55R35; Secondary 55R40, 55Q52
MathSciNet review: 1370636
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Abstract: We consider the homotopy type of classifying spaces $BG$, where $G$ is a finite $p$-group, and we study the question whether or not the mod $p$ cohomology of $BG$, as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of $BG$. This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of $BG$.


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Additional Information

Carlos Broto
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Email: broto@mat.uab.es

Ran Levi
Affiliation: Mathematisches Institut, Universität Heidelberg, INF 288, Heidelberg 69120, Germany
Address at time of publication: Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60201
Email: ran@math.nwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01692-9
PII: S 0002-9947(97)01692-9
Keywords: Classifying spaces, finite 2-groups, cohomology, Steenrod squares, Bockstein spectral sequence
Received by editor(s): May 19, 1995
Additional Notes: C. Broto is partially supported by DGICYT grant PB94-0725.
R. Levi is supported by a DFG grant.
Article copyright: © Copyright 1997 American Mathematical Society