Characters and automorphism groups of compact Riemann surfaces
Author(s)
Bibliographic Information
Characters and automorphism groups of compact Riemann surfaces
（London Mathematical Society lecture note series, 280）
Cambridge University Press, 2000
- : pbk
Available at 61 libraries
Note
Includes bibliographical references (p. [192]-195) and index
Description and Table of Contents
Description
This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra.
Table of Contents
- Preface
- Notation
- 1. Compact Riemann surfaces
- 2. Group characters
- 3. Automorphisms of compact Riemann surfaces
- 4. Generation of groups
- 5. Classification for small genus
- 6. Classification for fixed group: real characters
- 7. Classification for fixed group: nonreal irrationalities
- Appendix A. Abelian inariants
- Appendix B. Irreducible characters
- Appendix C. Maillet's determinant
- Bibliography
- Index.
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