Geometry of Principal Sheaves
март 2006 г. · Mathematics and Its Applications Книга 578 · Springer Science & Business Media
Электронная книга
444
Количество страниц
reportОценки и отзывы не проверены. Подробнее…
Об электронной книге
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.
Оцените электронную книгу
Поделитесь с нами своим мнением.
Где читать книги
Смартфоны и планшеты
Установите приложение Google Play Книги для Android или iPad/iPhone. Оно синхронизируется с вашим аккаунтом автоматически, и вы сможете читать любимые книги онлайн и офлайн где угодно.
Ноутбуки и настольные компьютеры
Слушайте аудиокниги из Google Play в веб-браузере на компьютере.
Устройства для чтения книг
Чтобы открыть книгу на таком устройстве для чтения, как Kobo, скачайте файл и добавьте его на устройство. Подробные инструкции можно найти в Справочном центре.
