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Determination of Grassmann Manifolds Which are Boundaries

Published online by Cambridge University Press:  20 November 2018

Parameswaran Sankaran
Parameswaran Sankaran*
Affiliation:
The Institute of Mathematical Sciences, C.I.T. Campus, Madras 600 113, India
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Abstract

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Let FGn,k denote the Grassmann manifold of all k-dimensional (left) F-vector subspace of Fn for F = ℝ, the reals, C, the complex numbers, or H the quaternions. The problem of determining which of the Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the case F = ℝ, including a sufficient condition, due to A. Dold, on n and k for ℝ Gn,k to bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well.

Keywords

57R75.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 119 - 122
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Conner, P. E., Differentiable periodic maps. 2nd ed., L.N.M. - 738, Springer-Verlag, 1979.Google Scholar
2. Lam, K. Y., A formula for the tangent bundle of flag manifolds and related manifolds, Trans. Amer. Math. Soc. 213 (1975), 305–314.Google Scholar
3. Milnor, J. W. and Stasheff, J. D., Characteristic classes, Ann. Math. Studies 76( 1974), Princeton Univ. Press, Princeton, N. J.Google Scholar
4. Sankaran, P., Which Grassmannians bound?, Arch. Math. 50 (1988), 474–476.Google Scholar
5 Sankaran, P., Cobordism of flag manifolds, submitted to Arch. Math.Google Scholar
6. Stong, R. E., Cup products in G rassmannians, Topology and App. 13 (1982), 103–113.Google Scholar