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The direct image of a vector bundle

Published online by Cambridge University Press:  24 October 2008

R. L. E. Schwarzenberger
Affiliation:
University of Warwick

Extract

It is well known that if M is a vector bundle over a space Y, and r: XY is a map, then there is an ‘induced’ vector bundle r*M over X. It is also known that a vector bundle L over X determines a ‘direct image’ vector bundle r* L over Y provided that r is a finite covering map ((1), § 1).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Atiyah, M. F.Characters and cohomology of finite groups. Inst. Hautes Études Sci. Publ. Math. 9 (1961).CrossRefGoogle Scholar
(2)Bourbaki, N.Intégration. Chaps. I–IV. Second edition (Hermann, Paris, 1965).Google Scholar
(3)Grauert, H.Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146 (1962), 331368.CrossRefGoogle Scholar
(4)Grothendieck, A.Éléments de géométrie algébrique. Chap. II, Étude globale élémentaire de quelques classes de morphismes. Inst. Hautes Études Sci. Publ. Math. 8 (1961).Google Scholar