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