|NOM DE FICHIER||Smooth Manifolds.pdf|
|TAILLE DU FICHIER||5,74 MB|
|DATE DE PUBLICATION||2015-Jan-14|
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 ...
manifolds), though we have eschewed PL manifolds in favor of smooth manifolds and often do not give results in their full generality. 1. Lecture 1: the theory of topological manifolds De nition 1.1. A topological manifold of dimension nis a second-countable Hausdor space Mthat is locally homeomorphic to an open subset of Rn. In this rst lecture, we will discuss what the \theory of topological ...