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This book gives a systematic account of the facts concerning complexes of differential operators on differentiable manifolds. The central place is occupied by the study of general complexes of differential operators between sections of vector bundles. Although the global situation often contains nothing new as compared with the local one (that is, complexes of partial differential operators on an open subset of ]Rn), the invariant language allows one to simplify the notation and to distinguish better the algebraic nature of some questions. In the last 2 decades within the general theory of...

This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications....

The main topic of this work is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one are often similar in content, the invariant language permits the simplification of the notation and more clearly reveals the algebraic structure of some questions.