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Towers of submanifolds of Grassmannians

Published online by Cambridge University Press:  14 November 2011

Elmer Rees
Elmer Rees
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh EH9 3JZ
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Synopsis

There is a conjecture that a tower of smooth subvarieties V(n) with fixed codimension l in Gk(ℂn) must be a standard example. It is shown that even under topological hypotheses, all cohomological invariants of such a tower must coincide with those of standard examples.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 153 - 156
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Adams, J. F.. Maps between classifying spaces II. Invent. Math. 49 (1978), 1–65.CrossRefGoogle Scholar
2Adams, J. F. and Mahmud, Z.. Maps between classifying spaces. Invent. Math. 35 (1976), 1–41.CrossRefGoogle Scholar
3Barth, W., Submanifolds of low codimension in projective space. Proceedings of the International Congress of Mathematicians (Vancouver 1974), Vol. 1, pp. 409–413. (Montreal: Canad. Math. Congress, 1975).Google Scholar
4Barth, W. and Van de Ven, A.. A decomposability criterion for algebraic 2-bundles in projective spaces. Invent. Math. 25 (1974), 91–106.CrossRefGoogle Scholar
5Barth, W. and Van de Ven, A.. On the geometry in codimension 2 of Grassmann manifolds. Lecture Notes in Mathematics 412, 1–35 (Berlin: Springer, 1975).Google Scholar
6Rees, E.. On submanifolds of projective space. J. London Math. Soc. 19 (1979), 159–162.CrossRefGoogle Scholar
7Sato, E.. On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties. J. Math. Kyoto Univ. 17 (1977), 127–150.Google Scholar
8Sato, E.. On infinitely extendable vector bundles on G/P. J. Math. Kyoto Univ. 19 (1979), 171–189.Google Scholar
9Sullivan, D.. Geometric Topology, Part I (Cambridge, Mass.: M.I.T., 1970).Google Scholar
10Thorn, R.. Quelques proprietes globales des variétés differentiables. Comment. Math. Helv. 28 (1954), 17–86.Google Scholar
11Tjurin, S. N.. Finite dimensional bundles on infinite varieties. Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), 1248–1268.Google Scholar
12Wilkerson, C.. Classifying spaces, Steenrod operations and algebraic closure. Topology 16 (1977), 227–237.CrossRefGoogle Scholar