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, 21,5 1 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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