Author | Maskit, Bernard. author |
---|---|
Title | Kleinian Groups [electronic resource] / by Bernard Maskit |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1988 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61590-0 |
Descript | XIII, 328 p. online resource |
I. Fractional Linear Transformations -- I.A. Basic Concepts -- I.B. Classification of Fractional Linear Transformations -- I.C. Isometric Circles -- I.D. Commutators -- I.E. Fractional Reflections -- I.F. Exercises -- II. Discontinuous Groups in the Plane -- II.A. Discontinuous Groups -- II.B. Area, Diameter, and Convergence -- II.C. Inequalities for Discrete Groups -- II.D. The Limit Set -- II.E. The Partition of C -- II.F. Riemann Surfaces -- II.G. Fundamental Domains -- II.H. The Ford Region -- II.I. Precisely Invariant Sets -- II.J. Isomorphisms -- II.K. Exercises -- II.L. Notes -- III. Covering Spaces -- III.A. Coverings -- III.B. Regular Coverings -- III.C. Lifting Loops and Regions -- III.D. Lifting Mappings -- III.E. Pairs of Regular Coverings -- III.F. Branched Regular Coverings -- III.G. Exercises -- IV. Groups of Isometries -- IV.A. The Basic Spaces and their Groups -- IV.B. Hyperbolic Geometry -- IV.C. Classification of Elements of Cn -- IV.D. Convex Sets -- IV.E. Discrete Groups of Isometries -- IV.F. Fundamental Polyhedrons -- IV.G. The Dirichlet and Ford Regions -- IV.H. Poincarรฉโs Polyhedron Theorem -- IV.I. Special Cases -- IV.J. Exercises -- IV.K. Notes -- V. The Geometric Basic Groups -- V.A. Basic Signatures -- V.B. Half-Turns -- V.C. The Finite Groups -- V.D. The Euclidean Groups -- V.E. Applications to Non-Elementary Groups -- V.F. Groups with Two Limit Points -- V.G. Fuchsian Groups -- V.H. Isomorphisms -- V.I. Exercises -- V.J. Notes -- VI. Geometrically Finite Groups -- VI. A. The Boundary at Infinity of a Fundamental Polyhedron -- VI.B. Points of Approximation -- VI.C. Action near the Limit Set -- VI.D. Essentially Compact 3-Manifolds -- VI.E. Applications -- VI.F. Exercises -- VI.G. Notes -- VII. Combination Theorems -- VII.A. Combinatorial Group Theory โ I -- VII.B. Blocks and Spanning Discs -- VII.C. The First Combination Theorem -- VII.D. Combinatorial Group Theory โ II -- VII.E. The Second Combination Theorem -- VII.F. Exercises -- VII.G. Notes -- VIII. A Trip to the Zoo -- VIII.A. The Circle Packing Trick -- VIII.B. Simultaneous Uniformization -- VIII.C. Elliptic Cyclic Constructions -- VIII.D. Fuchsian Groups of the Second Kind -- VIII.E. Loxodromic Cyclic Constructions -- VIII.F. Strings of Beads -- VIII.G. Miscellaneous Examples -- VIII.H. Exercises -- VIII.I. Notes -- IX. B-Groups -- IX.A. An Inequality -- IX.B. Similarities -- IX.C. Rigidity of Triangle Groups -- IX.D. B-Group Basics -- IX.E. An Isomorphism Theorem -- IX.F. Quasifuchsian Groups -- IX.G. Degenerate Groups -- IX.H. Groups with Accidental Parabolic Transformations -- IX.I. Exercises -- IX.J. Notes -- X. Function Groups -- X.A. The Planarity Theorem -- X.B. Panels Defined by Simple Loops -- X.C. Structure Subgroups -- X.D. Signatures -- X.E. Decomposition -- X.F. Existence -- X.G. Similarities and Deformations -- X.H. Schottky Groups -- X.I. Fuchsian Groups Revisited -- X.J. Exercises -- X.K. Notes -- Special Symbols