Basic Topology 2 : Topological Groups, Topology of Manifolds and Lie Groups

Adhikari, Avishek/ Adhikari, Mahima Ranjan

Springer Verlag, Singapore（2023/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 367 p.
• 言語 ENG
• 商品コード 9789811665790
• DDC分類 514

Full Description

This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.

Contents

1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.