466 Index
collared, 64
connected in dimension k, 10
constant fundamental group, 432
flat, xvi, 32, 201, 436
flat modulo A, 164
homotopically unknotted, 31
solvable, 158
spanned, 409
tame, 33
longitude, 28, 302, 329
Main Problem, xiv
manifold, 2
factor, 436
topological, 162
manifold-with-boundary, 2
map
r-connected, 185
1-UV, 168
proper, 58
mapping
cylinder, 123
neighborhood, 129, 417
reduced, 185
retraction, 186
simplicial, 124, 185
torus, 326
Matsumoto
link, 307
manifold, 333
Mazur swindle, 95
meets boundary regularly, 201
Menger
continuum, 138, 141, 233, 374
modified, 132
standard, 131
sponge, 131
meridian, 28, 302, 329
mesh of a cover, 137
metastable range, 192, 193
mildly wild arc, 79
Milnor
duality, 317
sequence, 276, 299
mismatch property, 413
modified Menger continuum, 132
Monotone Union Theorem, 285
Relative, 285
near-homeomorphism, 56
neighborhood, 2
of an end of a manifold, 428
of an end of a map, 432
Newman contractible manifold, 19
nice immersion, 228
nondegeneracy set, 58
null sequence, 372
one-point union, 1
one-sided, 350
orbit space, 413
order
ideal, 300
of a module, 300
ordinary polynomial, 312
organization of this book, xvi
orientable, 6
orientation, 405
orthogonal complement, 323
pillbox, 47
pinched
bicollar, 93
collar, 92
PL, xiv, xv
almost, 265
locally flat, 279, 402
modulo a point, 92
on an open subset, 265
Sch¨ onflies Conjecture, 26
Structure Theorem, 347
plug, 84
Poincar´ e Theorem
PL, 425
Weak, 99
Poincar´ e-Lefschetz duality, 6
polyhedron, xiv
presentation matrix, 300
preserve fibers, 209
primary
decomposition, 315
submodule, 314
Product Neighborhood Theorem, 201
Relative, 215
projective
class group, 430
module, 430
proper
mapping, 58
relation, 383
property 1-UV, 168
pseudo-isotopy, 154, 162
quotient map, 55
R-diameter, 385
R-disk, 385
radial engulfing, 123
ratio-changing general position, 151
regular neighborhood
-, 124
abstract, 213, 219
meets boundary regularly, 201
regular value, 225
relation, 383
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