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Hamiltonian Group Actions and Equivariant Cohomology

  • Shubham Dwivedi
  • Jonathan Herman
  • Lisa C. Jeffrey
  • Theo van den Hurk
Book

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 1-7
  3. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 9-15
  4. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 17-20
  5. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 21-26
  6. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 27-29
  7. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 31-46
  8. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 47-60
  9. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 61-70
  10. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 71-88
  11. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 89-102
  12. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 103-112
  13. Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
    Pages 113-122
  14. Back Matter
    Pages 123-132

About this book

Introduction

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.

Keywords

Symplectic geometry Equivariant cohomology Moduli spaces Flat connections Gauge theory

Authors and affiliations

  • Shubham Dwivedi
    • 1
  • Jonathan Herman
    • 2
  • Lisa C. Jeffrey
    • 3
  • Theo van den Hurk
    • 4
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Mathematical and Computational SciencesUniversity of Toronto at MississaugaMississaugaCanada
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada
  4. 4.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information