Titlebook: Smooth Manifolds and Observables; Jet Nestruev Textbook 2020Latest edition Springer Nature Switzerland AG 2020 Smooth manifolds.Smooth man

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Differential Forms: Classical and Algebraic Approach, generalized to become an inherent and very important part of the differential calculus over commutative algebras. The applications include the definition and study of symplectic, Poisson, and contact manifolds, Monge-Ampère equations, the Lie derivative, infinitesimal symmetries, derivations of vec

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Algebras and Points,ons can be identified with .. This involves giving the formal definition of the notion of . (which turns out to have a nontrivial structure!) and of the classes of .-algebras that need to be considered, in particular the so-called . and . ones.

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Smooth Maps,ons in the commutative algebra setting. This is done in the chapter. Numerous examples of general algebraic type, as well as of analytic coordinate type, are studied. The inverse and implicit function theorems are proved.

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Vector Bundles and Projective Modules,e of the category of vector bundles over a manifold and the category of projective finite-type modules over the correspondence algebra of smooth functions is established. The direct sum of vector bundles, their tensor product, subbundles, pullback vector bundles, sections of vector bundles, pseudo-bundles are considered.

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初学者

Spencer Complexes and Differential Forms,nics, is stressed. Another goal of the chapter is to demonstrate how to apply the typical manipulation techniques to concrete diffunctors and their representing objects. For this aim, in the first half of the chapter, the simpler diffunctors, related by Spencer complexes and by second-order differential forms, are studied in detail.

兵团

Points, Spectra and Ghosts,|, they are called .. Algebras not containing any invisible elements are called . .-. and are the most interesting ones. We also consider certain mysterious elements called . that appear in the algebra . of smooth functions on noncompact manifolds.

AROMA

Differential Calculus as Part of Commutative Algebra,e classical tools cannot be applied. The notions of tangent (co)vector and c(o)tangent manifold, of smooth map, of smooth (co)vector field, linear differential operator, and jet space, together with their basic properties, are described in the classical and in the general algebraic situations.