Book contents
- Frontmatter
- Dedication
- Contents
- Organization
- Acknowledgements
- 1 Introduction
- Part I Modular forms and their variants
- Part II Extensions and applications
- Part III Appendix
- Appendix A Some arithmetic
- Appendix B Riemann surfaces
- Appendix C Line bundles on Riemann surfaces
- Appendix D Riemann #-functions and meromorphic forms
- Appendix E Solutions to exercises
- References
- Index
Appendix B - Riemann surfaces
from Part III - Appendix
Published online by Cambridge University Press: 28 November 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Organization
- Acknowledgements
- 1 Introduction
- Part I Modular forms and their variants
- Part II Extensions and applications
- Part III Appendix
- Appendix A Some arithmetic
- Appendix B Riemann surfaces
- Appendix C Line bundles on Riemann surfaces
- Appendix D Riemann #-functions and meromorphic forms
- Appendix E Solutions to exercises
- References
- Index
Summary
A Riemann surface is a connected complex manifold of two real dimensions or equivalently a connected complex manifold of one complex dimension, also referred to as a complex curve. In this appendix, we shall review the topology of Riemann surfaces, their homotopy groups, homology groups, uniformization, construction in terms of Fuchsian groups, as well as their emergence from two-dimensional orientable Riemannian manifolds. All these ingredients provide crucial mathematical background for two-dimensional conformal field theory on higher genus Riemann surfaces and its application to string theory.
- Type
- Chapter
- Information
- Modular Forms and String Theory , pp. 362 - 377Publisher: Cambridge University PressPrint publication year: 2024