284 Index
bump function, 167
chain, 93, 96
chain complex, 92
for a triangulation, 94
chart, 104, 106, 109, 132
projection, 117
Christoffel symbol, 242
circle map, 145
classification, 29, 48, 53, 111
complex tori, 129
finitely generated abelian groups,
93
isometries of
H2,
204
matrices, 210
non-orientable surfaces, 91
orientable surfaces, 85
surfaces, 253
coarsening, 57, 60, 70
compact, 30
complete, 30
cone, 2, 22
conformal, 122, 128, 173, 181
conjugacy, 209
conjugate points, 177
connected, 30, 49
covering space, 83, 84
critical point, 14, 131, 150, 169, 259
degenerate, 141, 154
cross cap, see obius cap
cross-ratio, 193
crystallographic restriction, 45
curvature, 169, 182, 219, 233, 241
and angular excess, 238
Gaussian, 178, 241
principal, 241
cycle, 93, 96
cylinder, 2, 22
degree, 145, 151, 244, 267
in higher dimensions, 148
diffeomorphism, 51, 111, 249
and holomorphic equivalence,
125
differential equation, 158, 174, 234,
259, 266
dimension, 31, 32, 50
direct product, 47, 85, 160
disc model, 185, 197, 217, 232
ellipsoid, 3, 177
elliptic isometry, 205, 215
elliptic matrix, 210
elliptic plane, see projective plane
equidistant curve, 208, 214, 226,
252
Euler characteristic, 65, 73, 254,
269
and Betti numbers, 98
and continuous maps, 269
and curvature, 228
and Morse functions, 139
and vector fields, 259
combinatorial definition, 56
in higher dimensions, 270
modifying, 76, 82, 140
of covering space, 84
Euler-Lagrange equation, 170, 174,
176
exact sequence, 92
factor space, see quotient space
Fermi geodesic coordinates, 252
flow, 158
fractional linear transformation,
124, 183, 201
preserves cross-ratio, 193
fundamental domain, 10, 224, 227
fundamental group, 101, 256
Fundamental Theorem of Algebra,
246
Gauss-Bonnet Theorem, 229, 235,
239
genus, 99, 254
geodesic, 19, 20, 33, 170, 175, 186,
195, 206, 207, 226, 252, 268
geodesic flip, 45, 178
geodesic polar coordinates, 231,
236, 240
geographic coordinates, 16, 163
geometry, 2, 27, 127, 172, 259
glide reflection, 37
gradient, 152, 155
graph, 13
handle, 4, 74, 89, 250
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