You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Generalized Swan's Theorem and its Application
Proceedings of the American Mathematical Society
Vol. 123, No. 10 (Oct., 1995), pp. 3219-3223
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160685
Page Count: 5
You can always find the topics here!Topics: Differential operators, Mathematical theorems, Mathematical vectors, Morphisms, Mathematical manifolds, Topological theorems, Mathematical induction, Inverse functions, Taylor polynomials, Equivalence relation
Were these topics helpful?See somethings inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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.
Proceedings of the American Mathematical Society © 1995 American Mathematical Society