312 Index
deck group, 66, 71
deck transformation, 66
Dehn twist, 235
Dehn’s Dissection Theorem, 17, 98,
287
determinant, 30
diffeomorphism, 135
differential representation, 223
disk model, 125
disk rigidity, 177
disk-like sets, 143, 144
dodecahedron, 63
dot product, 22, 87
double octagon, 232
edges, 5
elliptic isometry, 130
equivalence class, 32
equivalence relation, 32
essential curves, 5
Euclidean cone, 207
Euclidean cone surface, 208
Euclidean plane, 1
Euclidean space, 1, 87
Euler characteristic, 37
exponential function, 175
faces, 5
Farey graph, 242, 245
Farey related, 242
figure 8, 69
flat cone surface, 207
flat torus, 16, 67, 195, 252
functoriality, 49
fundamental group, 43, 46, 71
Fundamental Theorem of Algebra,
57, 180
Gauss map, 239
Gauss–Bonnet Theorem, 107, 127
Gauss-Bonnet Theorem, 151
generalized circle, 116
geodesic, 145
geodesic half-plane, 150
geodesic hyperbolic triangle, 228
geodesic polygon, 127, 145
geodesic triangle, 107
geodesic triangulation, 150
geodesics, 9, 105, 120, 123
Giraud’s Theorem, 107
gluing, 2, 3, 31, 145
gluing recipe, 147
good metric space, 80
Green’s Theorem, 100, 166
group, 43
Hadamard’s Theorem, 154
harmonic function, 179
holomorphic function, 163
homeomorphism, 25
homomorphism, 44
homotopy, 45
homotopy equivalence, 45
Hopf–Rinow Theorem, 154
hyperbolic geometry, 9
hyperbolic group actions, 224
hyperbolic isometry, 121, 130, 143
hyperbolic plane, 9, 224
hyperbolic reflections, 229
hyperbolic surface, 143, 147, 195
ideal triangle, 127, 242
ideal vertices, 127
Implicit Function Theorem, 28
infimum, 31
infinite differentiability, 169
inner product, 121, 134
interior, 23
Invariance of Domain, 189
Inverse Function Theorem, 135, 185
irrational numbers, 247
isometry, 135
isomorphism, 44
isomorphism theorem, 71, 74, 79
Jordan curve, 199
Jordan domain, 199
Klein bottle, 35
latitude, 105
lens space, 59
Lie group, 30
lifting property, 73
line integrals, 98
linear fractional transformation, 11,
115, 130
linear functionals, 98
Previous Page Next Page