Piecewise Linear Topology

contents......Page 5
1 (page missing)......Page 7
2 Cell & simplicial complexes, subdivision......Page 10
3 Basic lemmas on subdivision......Page 15
4 PL maps, simplicial maps, subdivisions......Page 20
5 Piecewise linear manifolds......Page 25
6 Dual cells......Page 34
7 More lemmas (glueing, collars)......Page 38
8 Removing balls from spheres......Page 42
Appendix on convex cells......Page 46
1 Collapsing......Page 47
2 Full subcomplexes & derived neighborhoods......Page 54
3 Ambient isotopy......Page 58
4 Existence & uniqueness of regular neighborhoods......Page 62
5 Uniqueness of reg nbhds which meet the boundary regularly......Page 71
2 Triangulation of PL spaces and manifolds......Page 82
3 PL maps and subdivision theorems......Page 89
4 PL subspaces......Page 92
5 Collapsing and regular neighborhoods......Page 94
1 Definitions......Page 96
2 Approximation of continuous functions by PL maps......Page 97
3 Approximation of PL maps by nondegenerate PL maps......Page 100
4 Shifting subspaces to general position......Page 102
5 Shifting maps to general position......Page 105
1 Statement of the problem......Page 115
2 Sunny collapsing......Page 116
3 Factorization of collapses - proof of Theorem 1.2......Page 124
4 Unknotting ball pairs and sphere pairs......Page 127
5 Unknotting of embeddings of balls in balls......Page 132
1 Concordance, isotopy, isotopy by moves......Page 134
2 Locally unknotted manifold pairs & weak isotopy extension theorem......Page 140
3 Uniqueness of boundary collars & construction of compatible collars for manifold pairs......Page 144
4 The isotopy extension theorem......Page 153
5 The n-isotopy extension theorem......Page 159
2 Preliminary results......Page 166
3 Engulfing theorems, type (A)......Page 169
4 Engulfing theorems, type (B)......Page 173
5 Applications of engulfing......Page 175
1 relative the boundary......Page 180
2 modulo the boundary......Page 183
3 Embedding into a non-bounded manifold......Page 187
1 Intro......Page 189
2 Relative second derived neighborhoods......Page 190
3 The main lemma......Page 192
4 Proof of Theorems 9.1 and 9.2......Page 199
5 Extensions......Page 202
1 keeping the boundary fixed......Page 204
2 moving the boundary......Page 205
3 Unknotting in a manifold without boundary......Page 207
1 Linking numbers......Page 209
2 An obstruction to embedding and isotopy......Page 211
3 Obstruction to isotopy of embeddings of a manifold in euclidean space......Page 216
4 Other results......Page 222
1 Intro......Page 224
2 Lemma on homotopy groups of a triad......Page 225
3 Proof of Theorem 12.1......Page 227
1 Intro......Page 229
2 (boundary collar)......Page 233
3 (handle slides)......Page 234
4 (cancelling handles)......Page 237
5 (introducing handles)......Page 241
7 Geometric and algebraic intersections......Page 242
8 (cancelling 1-handles)......Page 251
9 Whitehead torsion of a handlebody decomposition......Page 254
10 Whitehead torsion......Page 257
11 (how many handles do we need?)......Page 274
12 h-Cobordisms with given torsion......Page 280
Bibliography......Page 284