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