Index 285
inverted, 79, 83
Hessian, 133, 170
holomorphic, 121
homeomorphism, 29, 51, 249
homology, 65, 92, 148
homothety, 108, 129, 182, 216
homotopy, 65, 87, 146, 154, 256
horocycle, 206, 213
hyperbolic isometry, 207, 216, 226
hyperbolic matrix, 210
hyperbolic plane, 181, 217, 225
hyperboloid, 239, 241
hypercircle, see equidistant curve
ideal boundary, 185, 211, 213
index
Morse, 141
of a continuous map, 267
of a curve, 152, 243, 250, 258
of a vector field, 151, 259
inner product, 160
integral curve, 158
isometry, 31, 34
orientation reversing, 199
isometry group, 44, 183, 211, 224,
227
Jordan Curve Theorem, 51, 249,
256
Klein bottle, 7, 24, 72, 264
lattice, 45
length, 170, 175, 181, 234
lift, 145
limit circle, see horocycle
Liouville’s theorem, 125
local coordinates, 13, 109, 155, 163
manifold, 49, 70
complex, 122
Riemannian, 161, 172
smooth, 103, 109, 251
map, 60, 67, 69, 229
homology of, 100
metric, 17
metric space, 28
metrisable, 49
obius cap, 80, 82, 91, 250
obius strip, 6, 18, 77, 80
obius transformation, see
fractional linear
transformation
modular surface, 129
Morse function, 136
Morse lemma, 134
neutral geometry, see absolute
geometry
norm, 170
normal subgroup, 211
orientability, 77, 81, 84, 88, 99, 113,
252
and homology, 100
osculating circle, 241
parabolic isometry, 206, 216
parabolic matrix, 210
parallel, 2, 212, 214
parallel postulate, 187, 198, 213
parametric representation
of curves, 22
of surfaces, 16, 27
partition of unity, 164, 165, 169,
266
patch, 104, 106, 163
Peano curve, 244
pencil, 206
planar model, 8, 69, 71, 73, 80, 224
notation, 72
smooth structure, 120
Poincar´ e conjecture, 90, 138
Poincar´ e duality, 270
Poincar´ e-Hopf Index Formula, 259
polarisation identity, 40
positive definite, 160, 162
pretzel, see surface of genus two
projective plane, 10, 18, 38, 66, 71,
269
pseudosphere, 186, 190
quotient space, 11, 260
smooth structure, 116, 118, 227
refinement, 61
reflection, 36
regular point, 14, 131
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