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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Real line bundles on spheres


Author: Allan L. Edelson
Journal: Proc. Amer. Math. Soc. 27 (1971), 579-583
MSC: Primary 55F15; Secondary 55F50
MathSciNet review: 0301016
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Abstract: In a recent paper the author proved a classification theorem for Atiyah-real vector bundles on spaces with free involutions. This result is now applied to the group of Atiyah-real line (i.e., one-dimensional) bundles on spheres, denoted $ {L_R}({S^n})$. It is proved that such bundles are classified by maps into a complex quadric $ Q{C^n}$. Using this classification it is proved that $ {L_R}({S^1}) = 0$ and that for $ n \geqq 3$ the groups are all isomorphic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0301016-8
PII: S 0002-9939(1971)0301016-8
Keywords: Atiyah-real vector bundle, conjugate linear isomorphism, equivariant homotopy, line bundle
Article copyright: © Copyright 1971 American Mathematical Society