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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

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