Generalized Swan’s theorem and its application
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- by P. Manoharan PDF
- Proc. Amer. Math. Soc. 123 (1995), 3219-3223 Request permission
Abstract:
Swan’s theorem verifies the equivalence between finitely generated projective modules over function algebras and smooth vector bundles. We define ${A^{(r)}}$-maps that correspond to usual non-linear differential operators of degree r under the equivalence of Swan’s theorem and thus generalize Swan’s theorem to include non-linear differential operators as morphisms. An ${A^{(r)}}$-manifold structure is introduced on the space of sections of a fiber bundle through charts with ${A^{(r)}}$-maps as transition homeomorphisms. A characterization for all the smooth maps between the spaces of sections of vector bundles, whose kth derivatives are linear differential operators of degree r in each variable, is given in terms of ${A^{(r)}}$-maps.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3219-3223
- MSC: Primary 58D15; Secondary 13C10, 55R10
- DOI: https://doi.org/10.1090/S0002-9939-1995-1264823-X
- MathSciNet review: 1264823