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Author: Efstathios Vassiliou Publisher: Springer Science & Business Media ISBN: 1402034164 Category : Mathematics Languages : en Pages : 454
Book Description
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
Author: Efstathios Vassiliou Publisher: Springer Science & Business Media ISBN: 1402034164 Category : Mathematics Languages : en Pages : 454
Book Description
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
Author: Anastasios Mallios Publisher: Springer Science & Business Media ISBN: 0817646345 Category : Mathematics Languages : en Pages : 244
Book Description
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author: Elemer Elad Rosinger Publisher: Springer Science & Business Media ISBN: 9780792352327 Category : Mathematics Languages : en Pages : 264
Book Description
Presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalized functions. This work addresses those who are interested in solving nonlinear PDEs, and in particular, in studying the Lie group symmetries of their classical or generalized solutions. This new method extends and completes earlier results of the author and collaborators, in which global Lie group actions on generalized functions were only defined in the case of projectable or fiber preserving Lie group actions. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Masaki Maruyama Publisher: CRC Press ISBN: 1000950700 Category : Mathematics Languages : en Pages : 324
Book Description
"Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."
Author: Anastasios Mallios Publisher: Springer Science & Business Media ISBN: 9780792350057 Category : Mathematics Languages : en Pages : 468
Book Description
This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
Author: Efstathios Vassiliou
Author: Efstathios Vassiliou
Author: Efstathios Vassiliou
Author: J. Szenthe
Author: Efstathios Vassiliou
Author: 
Author: Anastasios Mallios
Author: Elemer Elad Rosinger
Author: Masaki Maruyama
Author: 
Author: Anastasios Mallios