广义微分几何讲义 Lectures On Diffeology (Paperback) (ISBN-13: 9787523218419)

Lectures written by the leading figure in diffeology research

Brief Introduction

These lecture notes are intended for students interested in differential geometry, particularly in situations not covered by the classical theory. The first part is a series of lectures given at Shantou University as a special program. They introduce the main areas of differential geometry extended to diffeology, as developed in the chapters of the diffeology textbook. The second part consists of a series of notes and exercises chosen because they do not fall within the scope of the theory of manifolds. They illustrate some applications of diffeology: infinite spaces with singular quotients, symplectic diffeological space without Hamiltonian diffeomorphisms, general spaces of geodesics, Riemannian diffeology program, classifying space of quasi-spheres, and other examples. They have been chosen to familiarise the student with some specific techniques used in the versatile environment of diffeology.

Author Introduction

Patrick Iglesias-Zemmour is a researcher at the French National Center for Scientific Research (CNRS) and a long-term visiting professor at The Hebrew University of Jerusalem. He is renowned for his work in symplectic geometry and diffeology. His book Diffeology stands as the first international textbook in this field. Lectures on Diffeology offers a fresh presentation of his years of research achievements, complementing and echoing the content of Diffeology.

Diffeology研究领军人物所撰写的讲义

内容简介

《广义微分几何讲义》是为对微分几何感兴趣的学生准备的，尤其是那些在经典理论未涵盖的几何情形。它是已出版的《广义微分几何》（Diffeology）的配套教学笔记，一半源自作者在汕头大学访问时的专题讲座，一半则是作者在同各方学者多年研究探讨后的研究成果、思考、练习等作者希望与读者分享的笔记。全书以时间线为轴，讲述Diffeology领域的起源和发展，编排合理，每章篇头都有总述、定义、理论等讲解，辅以推论过程，由简到难，自然过渡到结论，很符合授课讲义的风格，其后还有习题、问题、思考探讨等用以巩固讲义知识，并启发思考，对研究微分几何或数学物理的学生与研究人员非常有用。

作者简介

帕特里克-伊格莱西亚斯-泽穆尔（Patrick Iglesias-Zemmour）是法国国家科学研究中心研究员，也是以色列希伯来大学的长期客座教授。他以辛几何和广义微分几何的研究而闻名。他所著的《广义微分几何》（Diffeology）是该领域国际上的首部教材。《广义微分几何讲义》是作者多年研究成果的全新呈现，与《广义微分几何》相互呼应。