Discontinuous groups of isometries in the hyperbolic plane / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt.

• I. Möbius transformations and non-euclidean geometry -- 1. Pencils of circles - inverse geometry -- 2. Cross-ratio -- 3. Möbius transformations, direct and reversed -- 4. Invariant points and classifications of Möbius transformations -- 5. Complex distance of two pairs of points -- 6. Non-euclidian metric -- 7. Isometric transformations -- 8. Non-euclidian trigonometry -- 9. Products and commutators of motions -- II. Discontinuous groups of motions and reversions -- 10. The concept of discontinuity -- 11. Groups with invariant points or lines -- 12. A discontinuity theorem -- 13. [F]-groups. Fundamental set and limit set -- 14.The convex domaqin of an [F]-group. Characteristic and isometric neighbourhood -- 15. Quasi-compactness modulo [F] and finite generation of [F] -- III. Surfaces associated with discontinuous groups -- 16. The surfaces [D] modulo [G] and [K]([F]) modulo [F] -- 17. Area and type numbers -- IV. Decomposition of groups -- 18. Composition of groups -- 19. Decomposition of groups -- 20. Decomposition of [F]-groups containing reflections -- 21. Elementary groups and elementrary surfaces -- 22. Complete decomposition and normal form in the case of quasi-compactness -- 23. Exhaustion in the case of non-quasi-compactness -- V. Isomorphism and homeomorphism -- 24. Topological and geometrical isomorphism -- 25. Topological and geometrical homeomorphism -- 26. Construction of g-mappings. Metric parameters. Congruent groups.

Ämnesord

Discontinuous groups  (LCSH)

Isometrics (Mathematics)  (LCSH)

Icke-euklidisk geometri  (sao)

Klassifikation

QA612.14 (LCC)

514/.2 (DDC)

Teh (kssb/7)

30F35 (msc)

51M10 (msc)