Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download C^\infinity - Differentiable Spaces PDF full book. Access full book title C^\infinity - Differentiable Spaces by Juan A. Navarro González. Download full books in PDF and EPUB format.
Author: Juan A. Navarro González Publisher: Springer Science & Business Media ISBN: 9783540200727 Category : Mathematics Languages : en Pages : 212
Book Description
The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Author: Juan A. Navarro González Publisher: Springer Science & Business Media ISBN: 9783540200727 Category : Mathematics Languages : en Pages : 212
Book Description
The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Author: Juan A. Navarro González Publisher: Springer ISBN: 3540396659 Category : Mathematics Languages : en Pages : 191
Book Description
The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Author: Dominic Joyce Publisher: American Mathematical Soc. ISBN: 1470436450 Category : Mathematics Languages : en Pages : 152
Book Description
If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.
Author: Jet Nestruev Publisher: Springer Nature ISBN: 3030456501 Category : Mathematics Languages : en Pages : 433
Book Description
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Author: Sheldon Axler Publisher: Springer Science & Business Media ISBN: 1475781377 Category : Mathematics Languages : en Pages : 266
Book Description
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Author: R. W. R. Darling Publisher: Cambridge University Press ISBN: 9780521468008 Category : Mathematics Languages : en Pages : 288
Book Description
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
Author: Loring W. Tu Publisher: Springer Science & Business Media ISBN: 1441974008 Category : Mathematics Languages : en Pages : 426
Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Nik Weaver Publisher: World Scientific ISBN: 9789810238735 Category : Mathematics Languages : en Pages : 242
Book Description
The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Author: Raoul Bott Publisher: Springer Science & Business Media ISBN: 1475739516 Category : Mathematics Languages : en Pages : 319
Book Description
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Author: Tristan Needham Publisher: Oxford University Press ISBN: 9780198534464 Category : Mathematics Languages : en Pages : 620
Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author: Juan A. Navarro González
Author: Juan A. Navarro González
Author: Juan A. Navarro González
Author: Dominic Joyce
Author: Jet Nestruev
Author: Sheldon Axler
Author: R. W. R. Darling
Author: Loring W. Tu
Author: Nik Weaver
Author: Raoul Bott
Author: Tristan Needham