Rank p − 1 mod-p H-spaces

Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p -local H -spaces of rank l < p − 1. The first construction goes through when l = p − 1 and we show the second does as well. However, the space produced need not be an H -space. We gi...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 194; no. 2; pp. 641 - 688
Main Authors Grbić, Jelena, Harper, John, Mimura, Mamoru, Theriault, Stephen, Wu, Jie
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2013
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Bottom Cell
Sphere Bundle
Whitehead Product
Homotopy Equivalent
Homotopy Inverse
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Summary:Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p -local H -spaces of rank l < p − 1. The first construction goes through when l = p − 1 and we show the second does as well. However, the space produced need not be an H -space. We give a criterion for when an H -space is obtained. In the special case of rank 2 mod-3 H -spaces, we also give a practical test for when the criterion holds, and use this to give many new examples of finite H -spaces.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-012-0085-1