286 Index
regularisation, 173
Riemann sphere, 123, 195
Riemann surface, 122
orientability, 124
Riemannian metric, 161, 169, 172
rotation, 35, 39, 129, 154, 185, 205,
215
saddle, 134, 140, 153
monkey, 143
scalar product, see inner product
Schoenflies Theorem, 249, 253
simplex, 53
skeleton, 87
skew, 2
sphere, 1, 18, 20, 38, 55, 65, 71,
114, 177, 269
Morse function, 135
stereographic projection, 15, 115,
123, 163
surface of genus two, 4, 118, 225,
227, 254
symmetric space, 46
synthetic geometry, 39, 198
tangent bundle, 155, 160
unit, 182
tangent space, 155, 160, 171
tangent vector, 43
Teichm¨ uller, 130, 228
Theorema Egregium, 242
topology, 2, 27, 28, 259
torus, 4, 56, 66, 69, 112, 116, 177,
264
complex, 126, 129
flat, 9, 26, 45, 47, 123, 224, 228
Morse function, 136
transition map, 104, 110, 113, 162
transitivity, 43, 127
translation, 36, 108, 182, 226
tree, 87
triangulation, 54, 67, 70, 253
and smooth structure, 112, 121,
229, 254
homology of, 94
orientable, 78
tubular neighbourhood, 251, 255
ultraparallel, 212, 214, 226
universal cover, 225
upper half-plane, 181, 190, 197,
214, 222
vector field, 150, 161, 259, 266
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