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

On totally geodesic spheres in Grassmannians and $ {\rm O}(n)$


Author: Qi Ming Wang
Journal: Proc. Amer. Math. Soc. 108 (1990), 811-815
MSC: Primary 53C42; Secondary 55P42, 57T20
MathSciNet review: 994793
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Abstract: It was shown in [5] that the generators of the homotopy groups of the stable orthogonal groups and the stable Grassmannians can be represented by embedded totally geodesic spheres of constant curvature. In this paper we prove that all elements of the above-mentioned homotopy groups can be represented by such spheres.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0994793-6
PII: S 0002-9939(1990)0994793-6
Keywords: Clifford modules, isoclinic spheres, KO groups, totally geodesic maps
Article copyright: © Copyright 1990 American Mathematical Society