The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

Karl H. Hofmann, Sidney A. Morris

• Publisher: De Gruyter
• Year: 2020
• Print ISBN: 9783110695953
• eBook ISBN: 9783110695991
• Edition: 4
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.

The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.

The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community.

Please submit any book proposals to Niels Jacob.

Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019)
Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)
Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020)
Mariusz Lema?czyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020)
Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021)
Miroslava Anti?, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021)
Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)
Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Table of contents

• Preface to the Fourth Edition
• Preface to the Second and Third Editions
• Preface to the First Edition
• The Logical Dependence of the Contents
• Contents
• Chapter 1. Basic Topics and Examples
• Chapter 2. The Basic Representation Theory of Compact Groups
• Chapter 3. The Ideas of Peter and Weyl
• Chapter 4. Characters
• Chapter 5. Linear Lie Groups
• Chapter 6. Compact Lie Groups
• Chapter 7. Duality of Abelian Topological Groups
• Chapter 8. Compact Abelian Groups
• Chapter 9. The Structure of Compact Groups
• Chapter 10. Compact Group Actions
• Chapter 11. The Structure of Free Compact Groups
• Chapter 12. Cardinal Invariants of Compact Groups
• Appendix 1. Abelian Groups
• Appendix 2. Covering Spaces and Groups
• Appendix 3. A Primer of Category Theory
• Appendix 4. Selected Results on Topology and Topological Groups
• Appendix 5. Measures on Compact Groups
• Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups
• Appendix 7. Weakly Complete Vector Spaces and Algebras
• References
• Index of Symbols
• Index