Fenchel, Werner, Nielsen, J. 　著

内容

目次

Editor's preface - Short biography of the authors - Mobiustransformations and non-euclidean geometry - Pencils of circles - Inversivegeometry - Cross-ratio - Mobius tranformations, direct and reversed -Invariant points and classification of Mobius transformations - Complexdistance of two pairs of points - Non-Euclidian metric - Geometrictransformations - Non-Euclidean trigonometry - Products and commutators ofmotions - Discontinuous groups of motions and reversions - The concept ofdiscontinuity - Groups with invariant points or lines - A discontinuitytheorem - F-groups. Fundamental set and limit set - The Convex domain ofF-group. Characteristic and isometric neighbourhood - Quasi-compactnessmodulo F and finite generation of F - Surfaces associated with discontinuousgroups - The surfaces D modulo G and K(F) modulo F - Area and type numbers -Decompositions of groups - Composition of groups - Decomposition of groups -Decompositions of F-groups containing reflections - Elementary groups andelementary surfaces - Complete decomposition and normal form in the case ofquasi-compactness - Exhaustion in the case of non-quasi-compactness -Isomorphism and homeomorphism - Topological and geometrical isomorphism -Topological and geometrical homeomorphism - Construction of g-mappings.Metric parameters. Congruent groups - Symbols and definitions - Bibliography