INDEX
Annulus Theorem, 154,157
Homotopy, 132,148
atoroidal,210
augmented characteristic pair
factor, 169
cable space, 188
carries a map, 132
characteristic pair, 172
augmented factor, 167
factor, 123
characteristic pair factor, 123
characteristic Seifert
pair, 172
characteristic simple pair, 211
complete system of disk, 44,57
complexity of map, 9
composing space, 188
compressible, 18,23,31
boundary, 36
connected sum, 18,26
co-product, 161
core, 124
decomposible homomorphism, 69
deficiency of group, 65
Dehn's Lemma, 3
Generalized, 6
ends
of a group, 127
of a pair, 127
of a space, 126
equivalent pairs, 164
essential
arc, 21
homomorphism, 69
map of pairs, 120
Essential Hoxnotopy Theorem, 132
exceptional
fiber, 84
point, 86
fiber
exceptional, 84,85
index, 84
preserving map, 84
fiber (continued)
regular, 84,85
fibered
neighborhood, 85
solid torus, 84
fills a surface, 132
finitely generated intersection
property, 75,114
geometric
almost, 81
manifold, 81
Haken-manifold, 42
Haken-number, 49
closed, 49,56
handle complexity, 61
Heegaard
genus, 20
splitting, 20
surface, 20,3 0
hierarchy, 21,51
length of , 5 1
partial, 51
homotopy
initial end of, 121
of pairs, 120
terminal end of, 121
homotopy equivalence, 227
splitting,227,228
Hopfian, 70
incompressible, 18,23,31
boundary, 37
indecomposible
cover, 69
homomo rphism, 6 9
inessential
arc, 21
homomorphism, 6 9
map of pairs, 120
injective, 33
I-pair, 130
product, 131
twisted, 131
irreducible, 18
250
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