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