Index
absolute value, 23, 362
action of a group, 185, 185–205,
248
adjacent tiles, 137, 137–146, 261
Alexander, James Waddell II
(1888–1971), 318
antilinear fractional map, 27,
27–33, 38, 186, 231–235
antipodal points, 49, 102
arc length, see length
area, 131
hyperbolic area, 43, 43–44
spherical area, 53, 182
B2,
the disk model for the
hyperbolic plane, 36, 36–39,
43, 44, 101, 158–160, 209, 212,
216, 223
Bd(P, r), a ball in a metric space, 4
ball
ball in
R3,
5, 344
ball in a metric space, 4, 42–43,
68–79, 240, 262
ball model for the hyperbolic
space, 236, 240
belong to, 355
bijection, 5, 90, 185, 357
bijective, 357
Bonahon, Francis, iii
Bonnet, Pierre Ossian (1819–1892),
131
boundary
boundary of a manifold, 348
boundary point, 152
bounded, 62, 81, 152, 152–161
Brock, Jeffrey F., 283
Bromberg, Kenneth W., 282
Busemann
Busemann function, 178, 183
Busemann, Herbert (1905–1994),
178
C, the set of all complex numbers,
356, 361–364
Canary, Richard D., 283
Cannon, James W., 302
canonical tile, 143, 143–146
Cauchy
Cauchy sequence, 135, 182
Cauchy, Augustin (1789–1857),
182, 211
Cayley, Arthur (1821–1895), 45
center
center of a horocircle, 172, 214
center of a horosphere, 234
Cerf, Jean, 318
circle, 5, 17–22, 32–33, 38, 48,
85–87, 172, 207–212, 230, 288,
317
377
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