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General theory

by Antonio Kumpera and Donald Spencer

(Annals of mathematics studies, no. 73 . Lie equations / by Antonio Kumpera and Donald Spencer ; v. 1)(Tokyo University international edition, no. 72)

The Univ. Press, 1972

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Note

Originally published:Princeton University Press and the University of Tokyo Press,1972

Original series:Annals of Mathematics Studies, no.73

Description and Table of Contents

Description

In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.

Table of Contents

*Frontmatter, pg. i*Foreword, pg. v*Glossary of Symbols, pg. ix*Table of Contents, pg. xiii*Introduction, pg. 1*A. Integrability of Lie Structures, pg. 7*B. Deformation Theory of Lie Structures, pg. 29*Chapter I. Jet Sheaves and Differential Equations, pg. 49*Chapter II. Linear Lie Equations, pg. 88*Chapter III. Derivations and Brackets, pg. 104*Chapter IV. Non-Linear Complexes, pg. 136*Chapter V. Derivations of Jet Forms, pg. 212*Appendix. Lie Groupoids, pg. 257*References, pg. 278*Index, pg. 286

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