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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