Index ancestor, 97 of an edge, 11 atom, 63 vanishing, 102 basic path, 65 bead, 63, 72, 98 bitten, 105 consumed, 105 fast, slow, 104 unbounded, 118 vanishing, 102 bead norm, 107 Beaded Decomposition Theorem, 63, 72, 88 biting, 105 blocks B, 54 bonus scheme, 51, 138 Bounded Cancellation Lemma, 10, 97 Bounded Singularities Lemma, 8 Bracketing Theorem, xi, 141 Buffer Lemma, 26, 122 relative, 122 weighted, 123 colour of an edge, 11, 97 colours adjacent, 19 consumed, 23 essentially adjacent, 28 resuscitated, 126 unnamed, 127 corridor, 5, 6, 96 bead-length of, 99 chromatic decomposition of, 18, 108 first decomposition of, 17, 108 length of, 6, 12, 100 time-flow of, 10 corridor length function, 142 death (of an edge), 7 Dehn function, 3, 95 edge cancelled, 16 consumed, 16 displayed, 101 indistinguishable, 112 linear robust past of, 113 new, 16 old, 16 parabolic, 113 end stability, 102 family forest, 11, 38, 77, 97 future highlighted, 21 nibbled, 72, 83, 91 of a bead, 99 of an edge, 11, 97 para-preferred, 15 preferred, 14, 103–105 robust, 113 semi-naive, 104 swollen, 52, 115, 138 tenuous, 105 growing exceptional path (GEP), 62 hard splitting, 62 HNP biting, 112 HNP cancellation, 110 implosive array, 28, 30, 127 HNP, 128 isoperimetric inequality, 3, 95 letter constant, fast, slow, 15 exponential, 13 non-constant, 17 para-linear, 15 parabolic, 13 mapping torus, 96, 98 naive expansion, 7 neutering, 26, 32 stable, 123 weighted, 125 151
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