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Some non-embedding theorems for the Grassmann manifolds G2,n and G3,n

Published online by Cambridge University Press:  20 January 2009

V. Oproiu
Affiliation:
Department of Mathematics, Iasi University, Romania
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In recent years, the problem of embedding the projective spaces in Euclidean spaces was studied very much, by different methods. Usually, the negative results on the embedding problem are proved by using suitable homotopy invariants. The best known example of such homotopy invariants is given by the Stiefel–Whitney classes.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(1) Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces, Amer. J. Math. part 180 (1958), 459-538; part II81 (1959), 315–382; part III 82 (1960), 491504.Google Scholar
(2) Chern, S. S., On the multiplication in the characteristic ring of a sphere bundle, Ann. of Math. 49 (1948), 362372.CrossRefGoogle Scholar
(3) Chern, S. S., Topics in differential geometry, Mimeographed notes (Institute for Advanced Study, Princeton, 1951).Google Scholar
(4) Hoggar, S. G., A non-embedding result for complex Grassmann manifolds, Proc. Edinburgh Math. Soc. 17 (1970-1971), 149153.CrossRefGoogle Scholar
(5) Hirzebruch, F., Topological methods in algebraic geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
(6) Hsiang, W. C. and Szczarba, R. H., On the tangent bundle of a Grassman manifold. Amer. J. Math. 86 (1964), 698704.CrossRefGoogle Scholar
(7) Milnor, J., Lectures on Characteristic Classes, Mimeographed lecture notes (Princeton University, 1957).Google Scholar
(8) Porteous, I. R., Topological geometry (Van Nostrand, 1969).Google Scholar
(9) Thomas, E., On tensor product of n-plane bundles, Arch. Math. (Basel) 10 (1959), 174179.CrossRefGoogle Scholar