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Transactions of the American Mathematical Society

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



Spaces which look like quaternionic projective $n$-space

Author: C. A. McGibbon
Journal: Trans. Amer. Math. Soc. 272 (1982), 569-587
MSC: Primary 55R35
MathSciNet review: 662054
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Abstract: The projective $n$-spaces which correspond to the various multiplicative structures on the three sphere are studied. Necessary and sufficient conditions for a projective $n$-space to extend to a projective $n+1$-space are described. At each odd prime, an infinite family of exotic projective spaces is constructed. These exotic spaces are not homotopy equivalent, at the prime in question, to the classical quaternionic projective $n$-space. It is also shown that these exotic projective $n$-spaces do not occur as the finite skeleton of a classifying space for a group with the homotopy type of the three sphere.

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Keywords: Projective <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-space, classifying space, Whitehead product, Stasheff’s <IMG WIDTH="32" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img16.gif" ALT="$A_n$">-structures, Toda’s alpha family
Article copyright: © Copyright 1982 American Mathematical Society