Index Accepted (word), 198 Ackermann function, 53 Arrow (of an automaton), 198 Archimedian (group), 29 Artin coordinates (of a braid), 275 group, see Artin–Tits group representation, 174 Artin–Tits group, 301 spherical, 302 Automaton, 198 Base, 214 Bi-ordering, see ordering Bi-orderable (group), 20 Blueprint (term), 79 Braid, 9 dangerous, 167 dual — monoid, 156 dual-simple, 156 geometric, 10 group, 9 — of a surface, 302 monoid, 14 palindromic, 49 parenthesized, 306 positive, 14 pure, 273 quasi-positive, 28 σ-negative, σ-positive, 23 σ i -free, σ-, σ i -negative, σ i -positive, 23 σΦ-negative, σΦ-positive, 24 simple, 108 special, 59 Braid word, 9 drawn in X, 93 dual, 158 equivalent, 9 greedy normal, 109 σ 1 -free, 20 σ-negative, σ-positive, 20 σ i -negative, σ i -positive, 22 σΦ-negative, σΦ-positive, 24 σΦ-nonnegative, i 166 reducible, 88 representative, 9 Breadth φn-breadth, 159 Φn-breadth, 134 Cantor set, 266 Cayley graph, 93 Class (shi-class), 121 Code (of a 3-strand braid), 136 Colouring (braid diagram), 56 Combinatorial type of a triangulation, 236 of a flip, 242 Combing, of a pure braid, 275 of a triangulation, 241 Comparison (Property), 60 Complexity (ATH), 212 (braid), 206 (curve diagram), 199 Cone (positive), 20 Conradian (group), 27 Content, 101 Convex (subgroup), 34 Coordinates of a braid, 222, 223 unreduced, 232 reduced, 234 of a lamination, 230 Curve diagram, 186 isotopic, 186 positive, 201 Curve system, 228 normal, 228 Cycling (automorphism), 14 D-disk (of a pair of triangulations), 237 Decomposition, 133 Defect (pseudo-character), 48 Degree (of a braid), 109 Dehn half-twist, 192 Denominator (of a transmission), 209 Dense (ordered group), 31 321

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