Characters and automorphism groups of compact Riemann surfaces

Author(s)

    • Breuer, Thomas

Bibliographic Information

Characters and automorphism groups of compact Riemann surfaces

Thomas Breuer

（London Mathematical Society lecture note series, 280）

Cambridge University Press, 2000

  • : pbk

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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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