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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