Piecewise linear topology

Description

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