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COMMENSURABLE GROUPS OF MOEBIUS TRANSFORMATIONS

  • Leon Greenberg
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Discontinuous Groups and Riemann Surfaces (AM-79), Volume 79
This chapter is in the book Discontinuous Groups and Riemann Surfaces (AM-79), Volume 79
© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  1. Frontmatter i
  2. PREFACE v
  3. CONTENTS vii
  4. CONSTRUCT ABILITY AND BERS STABILITY OF KLEINIAN GROUPS 1
  5. ALGEBRAIC CURVES AND HALF-CANONICAL LINEAR SERIES 13
  6. SUFFICIENT CONDITIONS FOR QUASI-CONFORMAL EXTENSION 23
  7. FUNDAMENTAL DOMAINS FOR KLEINIAN GROUPS 31
  8. SPACES OF DEGENERATING RIEMANN SURFACES 43
  9. MAPPING CLASS GROUPS OF SURFACES: A SURVEY 57
  10. A NOTE ON L2 ( Γ \ G ) 73
  11. ON THE OUTRADIUS OF FINITE-DIMENSIONAL TEICHMÜLLER SPACES 75
  12. SOME DIRECT LIMITS OF PRIMITIVE HOMOTOPY WORDS AND OF MARKOFF GEODESICS 81
  13. ON THE CARATHÉODORY METRIC IN TEICHMÜLLER SPACES 99
  14. SOME REFINEMENTS OF THE POINCARÉ PERIOD RELATION 105
  15. REMARKS ON AUTOMORPHISMS OF COMPACT RIEMANN SURFACES 121
  16. THE STRUCTURE OF PSL2(R );R , THE RING OF INTEGERS IN A EUCLIDEAN QUADRATIC IMAGINARY NUMBER FIELD 145
  17. QUASI-CONFORMAL MAPPINGS AND LEBESGUE DENSITY 171
  18. ON THE MODULI OF COMPACT RIEMANN SURFACES WITH A FINITE NUMBER OF PUNCTURES 181
  19. MAXIMAL GROUPS AND SIGNATURES 207
  20. COMMENSURABLE GROUPS OF MOEBIUS TRANSFORMATIONS 227
  21. CHABAUTY SPACES OF DISCRETE GROUPS 239
  22. MONODROMY GROUPS AND LINEARLY POLYMORPHIC FUNCTIONS 247
  23. COLLARS ON RIEMANN SURFACES 263
  24. DEFORMATIONS OF CERTAIN COMPLEX MANIFOLDS 269
  25. ON THE A (Γ ) ⊂ Bq(Γ ) CONJECTURE FOR INFINITELY GENERATED GROUPS 283
  26. THE FUNDAMENTAL GROUPS OF CERTAIN SUBGROUP SPACES 289
  27. MODULAR GROUPS AND FIBER SPACES OVER TEICHMÜLLER SPACES 297
  28. UNIVERSAL PROPERTIES OF FUCHSIAN GROUPS IN THE POINCARÉ METRIC 315
  29. REMARKS ON COMPLEX MULTIPLICATION AND SINGULAR RIEMANN MATRICES 341
  30. INTERSECTIONS OF COMPONENT SUBGROUPS OF KLEINIAN GROUPS 349
  31. POLYNOMIAL APPROXIMATION IN THE BERS SPACES 369
  32. SIMPLE ILLUSTRATIONS OF THE USES OF EXPLICIT COMPUTATION OF THETA CONSTANTS 379
  33. ON THE RELATION BETWEEN LOCAL AND GLOBAL PROPERTIES OF BOUNDARY VALUES FOR EXTREMAL QUASI-CONFORMAL MAPPINGS 391
  34. SYMMETRIC EMBEDDINGS OF RIEMANN SURFACES 409
  35. ON THE TRAJECTORY STRUCTURE OF QUADRATIC DIFFERENTIALS 419
  36. THE MAXIMAL INSCRIBED BALL OF A FUCHSIAN GROUP 439
  37. Backmatter 445
https://doi.org/10.1515/9781400881642-018

Chapters in this book

  1. Frontmatter i
  2. PREFACE v
  3. CONTENTS vii
  4. CONSTRUCT ABILITY AND BERS STABILITY OF KLEINIAN GROUPS 1
  5. ALGEBRAIC CURVES AND HALF-CANONICAL LINEAR SERIES 13
  6. SUFFICIENT CONDITIONS FOR QUASI-CONFORMAL EXTENSION 23
  7. FUNDAMENTAL DOMAINS FOR KLEINIAN GROUPS 31
  8. SPACES OF DEGENERATING RIEMANN SURFACES 43
  9. MAPPING CLASS GROUPS OF SURFACES: A SURVEY 57
  10. A NOTE ON L2 ( Γ \ G ) 73
  11. ON THE OUTRADIUS OF FINITE-DIMENSIONAL TEICHMÜLLER SPACES 75
  12. SOME DIRECT LIMITS OF PRIMITIVE HOMOTOPY WORDS AND OF MARKOFF GEODESICS 81
  13. ON THE CARATHÉODORY METRIC IN TEICHMÜLLER SPACES 99
  14. SOME REFINEMENTS OF THE POINCARÉ PERIOD RELATION 105
  15. REMARKS ON AUTOMORPHISMS OF COMPACT RIEMANN SURFACES 121
  16. THE STRUCTURE OF PSL2(R );R , THE RING OF INTEGERS IN A EUCLIDEAN QUADRATIC IMAGINARY NUMBER FIELD 145
  17. QUASI-CONFORMAL MAPPINGS AND LEBESGUE DENSITY 171
  18. ON THE MODULI OF COMPACT RIEMANN SURFACES WITH A FINITE NUMBER OF PUNCTURES 181
  19. MAXIMAL GROUPS AND SIGNATURES 207
  20. COMMENSURABLE GROUPS OF MOEBIUS TRANSFORMATIONS 227
  21. CHABAUTY SPACES OF DISCRETE GROUPS 239
  22. MONODROMY GROUPS AND LINEARLY POLYMORPHIC FUNCTIONS 247
  23. COLLARS ON RIEMANN SURFACES 263
  24. DEFORMATIONS OF CERTAIN COMPLEX MANIFOLDS 269
  25. ON THE A (Γ ) ⊂ Bq(Γ ) CONJECTURE FOR INFINITELY GENERATED GROUPS 283
  26. THE FUNDAMENTAL GROUPS OF CERTAIN SUBGROUP SPACES 289
  27. MODULAR GROUPS AND FIBER SPACES OVER TEICHMÜLLER SPACES 297
  28. UNIVERSAL PROPERTIES OF FUCHSIAN GROUPS IN THE POINCARÉ METRIC 315
  29. REMARKS ON COMPLEX MULTIPLICATION AND SINGULAR RIEMANN MATRICES 341
  30. INTERSECTIONS OF COMPONENT SUBGROUPS OF KLEINIAN GROUPS 349
  31. POLYNOMIAL APPROXIMATION IN THE BERS SPACES 369
  32. SIMPLE ILLUSTRATIONS OF THE USES OF EXPLICIT COMPUTATION OF THETA CONSTANTS 379
  33. ON THE RELATION BETWEEN LOCAL AND GLOBAL PROPERTIES OF BOUNDARY VALUES FOR EXTREMAL QUASI-CONFORMAL MAPPINGS 391
  34. SYMMETRIC EMBEDDINGS OF RIEMANN SURFACES 409
  35. ON THE TRAJECTORY STRUCTURE OF QUADRATIC DIFFERENTIALS 419
  36. THE MAXIMAL INSCRIBED BALL OF A FUCHSIAN GROUP 439
  37. Backmatter 445
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