Foundations of Hyperbolic ManifoldsSpringer Science & Business Media, 23.08.2006 - 782 Seiten This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately. |
Inhalt
Euclidean Geometry | 1 |
Spherical Geometry | 35 |
Hyperbolic Geometry | 54 |
Inversive Geometry | 100 |
Isometries of Hyperbolic Space | 144 |
Geometry of Discrete Groups | 188 |
Classical Discrete Groups | 263 |
Geometric Manifolds | 334 |
Geometric Surfaces | 375 |
Hyperbolic 3Manifolds | 435 |
Hyperbolic nManifolds | 508 |
Geometrically Finite nManifolds | 600 |
Geometric Orbifolds | 681 |
745 | |
768 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
assume bijection closed compact conjugate contains convex polyhedron convex subset cosh crystallographic group curve cusp point cycle defined Definition dihedral angles discrete group discrete subgroup disjoint elliptic Euclidean Figure formula function fundamental polyhedron G)-orbifold G)-path geodesic arc geodesic line geodesic segment geometrically finite geometry group of isometries Hence homeomorphism homotopy horoball hyperbolic 3-manifold hyperbolic line hyperbolic triangle hyperplane ideal vertex induces integer intersection invariant isomorphism Lemma Let G limit point local isometry locally finite Lorentz m-plane manifolds Math matrix metric space Möbius transformation Moreover n-dimensional n-simplex n-space nonempty orbifold orientable orthogonal paper parabolic Poincaré polygon polyhedra polyhedron polytope proof of Theorem Prove quotient map real number reflection group regular polytopes Rn+1 sequence side-pairing sides sinh space-form sphere spherical subgroup of M(B Suppose tessellation Theorem time-like topological group topology unique vertices