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

σ1-free, 20

σ-negative, σ-positive, 20

σi-negative, σi-positive, 22

σΦ-negative, σΦ-positive, 24

σi Φ-nonnegative, 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