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Involutive Property of Resolutions of Differential Operators

Published online by Cambridge University Press:  22 January 2016

Masatake Kuranishi
Masatake Kuranishi*
Affiliation:
Columbia University, New York, NY.U.S.A.
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Let E and E′ be C∞ vector bundles over a C∞ manifold M. Denote by Γ(E) (resp. by Γ(E′) the vector space of C∞ cross-sections of E (resp. of E′) over M. Take a linear differential operator of the first order D: Γ(E) → Γ(E′) induced by a vector bundle mapping σ(D): jl(E) ′ E′, where Jk(E) denotes the vector bundle of k-jets of cross-sections of E.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 419 - 427
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bott, R., Spencer Resolution, Mimeographed Note, Harward Univ., 1963.Google Scholar
[2] Griffiths, P., On the Theory of Variation of Structures defined by Transitive Continuous Pseudogroups, Osaka Journ. of Math., 1964, 175–199.Google Scholar
[3] Guillemin, V. and Sternberg, S., An Algebraic Model of Transitive Differential Geometry, Bull, of the Amer. Math. Soc., 70 (1964), 16–47.Google Scholar
[4] Guillemin, V. and Sternberg, S., Deformation of Pseudogroups, Mimeographed Note, Harvard Univ., 1964.Google Scholar
[5] Kuranishi, M., On Resolution of Sheaves defind by Partiel Differential Equations, Amer. Journ., (1964), 379–391.Google Scholar
[6] Quillen, D., Thesis, Harvard University, 1963.Google Scholar
[7] Singer, I. M. and Sternberg, S., On the Infinite Groups of Lie and Cartan, I. Journ. D’Analyse Math., (1965), 1–114.Google Scholar
[8] Spencer, D. C., Deformations of Structures on Manifolds defined by transitive, Continuous Pseudogroups, Ann. of Math., 76 (1962), 306–445.Google Scholar