|
ИСТИНА |
Войти в систему Регистрация |
ФНКЦ РР |
||
Introduction to differential topologyучебный курс
- Автор: Мищенко А.С.
- Год создания: 2015
- Организация: МГУ имени М.В. Ломоносова
- Курс на иностранном языке
- Описание: Differential topology may be defined as the study of those properties of differentiable manifolds which are invariant under diffeomorphism (differentiable homeomorphism). Typical problem falling under this heading are the following: 1) Given two differentiable manifolds, under what conditions are they diffeomorphic? 2) Given a differentiable manifold, is it the boundary of some differentiable manifold-with- boundary? 3) Given a differentiable manifold, is it parallelisable? All these problems concern more than the topology of the manifold, yet they do not belong to differential geometry, which usually assumes additional structure (e.g., a connection or a metric). The most powerful tools in this subject have been derived from the methods of algebraic topology. In particular, the theory of characteristic classes is crucial, where-by one passes from the manifold M to its tangent bundle, and thence to a cohomology class in M which depends on this bundle.
- Добавил в систему: Мищенко Александр Сергеевич
Преподавание курса
- 8 августа 2015 - 31 августа 2015 Мищенко Александр Сергеевич
- МГУ имени М.В. Ломоносова, Механико-математический факультет
- в Harbin Institute of Technology (международная организация, университет, Китай)
- факультативная, лекции, 24 часов
- Автор: Мищенко А.С.