Overview
- Self-contained treatment of equivariant cohomology
- Treatment of moduli spaces of flat connections (a topic of considerable current interest)
- The only background required is a course on differential manifolds (a standard offering at the advanced undergraduate or introductory graduate level)
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
Keywords
About this book
This monograph could be used for a graduate course on symplectic geometry as well as for independent study.
The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Reviews
Authors and Affiliations
Bibliographic Information
Book Title: Hamiltonian Group Actions and Equivariant Cohomology
Authors: Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-27227-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-27226-5Published: 07 October 2019
eBook ISBN: 978-3-030-27227-2Published: 23 September 2019
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XI, 132
Number of Illustrations: 2 b/w illustrations, 1 illustrations in colour