464 Index

resolution, 434

set, 107

Cell-like Approximation Theorem, 366

cellular, 59

map, 60

move, 146

set, 59

cellularity criterion, 73, 106

center line of a solid torus, 44

closed

n-cell complement, 410

manifold, 2

cocore of a handle, 329

codimension, xvii

collapse, 100

(j, )−, 254

collar

for an end, 428

of a ball pair, 285

of a subset, 64

pinched, 92

singular, 405

complementary domains, 26

completion

of a manifold, 428

of map, 432

complex

CW, xiv

simplicial, xiv

concordance, 198

concordant, 199

Cone Unknotting Theorem, 201

Relative, 215

connected

k-connected pair, 11

k-connected space, 10

locally k-co-connected, 31

locally k-connected, 10

continuous relation, 383

contractible retraction, 213

controlled engulfing, 115

generalized, 119, 213, 262, 266, 354, 359,

362

coordinate neighborhood, xiv

core of a handle, 329

covering isotopy, 209

Theorem

Relative, 216

theorem, 210

covering transformations, 298

cube, 1, 131

crumpled, 410

with handles, 84

CW complex, xiv

DDP, 367

deck transformations, 298

decomposition space, 55

deficiency of a group, 283

defining sequence

abstract, 172

compatible, 176

geometric, 173

degree, 405

of a Laurent polynomial, 312

Dehn’s Theorem, 282

Delta structure, 236, 388

(δ, h)-cobordism over X, 433

δ-homotopy, 118

δ-product structure over X, 433

demension, 125

diameter of a homotopy, 432

dimension

of a topological space, 14

of embedding, 125

theorem, 8

disjoint disks property, 367

disk, 1

bundle neighborhood, 346

dominated by a finite complex, 429

double Fox-Artin arc, 77

Double Suspension Theorem, 423, 443

dual

face of a cube, 133

skeleton of a cube, 133

skeleton of a triangulation, 98

Duality Theorem, 6, 8, 317

dunce hat, 189

embedded space, xiv

embedding, xiv

dimension, 125, 160

relation, 383

cell-like, 383

Embedding Existence Theorems, 162, 182,

185, 190, 191, 194, 217, 237, 274, 290,

325, 327, 335, 391, 438

end

of a manifold, 428

of a map, 432

End Theorem, 433

engulfing, 97

Bryant-Seebeck, 115

controlled, 115

generalized, 119

radial, 123

Stallings, 99

Zeeman, 105

-mapping, 14

-mapping cylinder neighborhood, 129

-push, 115

-regular neighborhood, 124

-tame, 157

equivalent