The Geometric Topology of 3-manifolds, Том 40American Mathematical Soc., 31 дек. 1983 г. - Всего страниц: 238 This book belongs in both graduate and undergraduate libraries as a useful reference for students and researchers in topology. It is directed toward mathematicians interested in geometry who have had at least a beginning course in topology. It should provide the reader with a better understanding of the physical properties of Euclidean 3-space--the space in which we presume we live. The reader should learn of some unsolved problems that continue to baffle reseachers. The most profound result in the volume is the side approximation theorem. However, some of the preliminary results and some of the applications may be used more frequently for reference. |
Содержание
| 1 | |
| 2 | |
| 4 | |
| 6 | |
Chapter 1 PL Planar Maps 1 Linear maps | 9 |
PL maps | 11 |
Pushes | 13 |
Isotopies | 15 |
Linking l Chains cycles bounding cycles | 105 |
Linking polygons | 108 |
Linking curves | 109 |
Balls do not link | 111 |
Nonlinking curves | 112 |
Homology groups | 113 |
Separation 1 General position approximations | 115 |
Separation by spheres | 117 |
Meshing triangulations | 17 |
The Schoenflies Theorem | 19 |
PL Schoenflies theorem i | 22 |
Skew sets | 23 |
No arc separates R2 | 26 |
JordanBrouwer theorem | 27 |
Schoenflies theorem | 29 |
Wild 2Spheres l Tame and wild 2spheres | 33 |
3spheres | 34 |
Alexander horned sphere | 38 |
Simple connectivity | 41 |
Solid Alexander horned sphere | 42 |
Peculiar involutions | 43 |
Antoines necklace | 44 |
An Antoine wild sphere | 47 |
Bings hooked rug _ | 53 |
The Generalized Schoenflies Theorem 1 Schoenflies theorem for a 2sphere | 57 |
Canonical collared Schoenflies theorem | 62 |
Local flatness | 64 |
Weakness of the generalized Schoenflies theorem | 67 |
The Fundamental Group 1 Paths and loops | 69 |
The fundamental group | 72 |
Graphs | 73 |
Associating words with loops | 74 |
Relations | 78 |
Shelling | 80 |
Presentations of groups | 83 |
Short cuts | 84 |
Why compute fundamental groups | 88 |
A homotopy cube | 94 |
Other treatments | 95 |
Chapter VI Mapping onto Spheres l Retractions onto boundaries | 97 |
ARs and ANRs | 98 |
Inessential mappings | 99 |
Projections | 101 |
Fixed points | 102 |
JordanBrouwer theorem | 118 |
Local separation 11 | 119 |
Pulling Back Feclcrs | 121 |
Pullback theorems | 123 |
Reimbedding a crumpled cube | 126 |
Repeated pullbacks | 127 |
Sewing cubes together | 128 |
Pulling feelers off a null sequence of disks | 129 |
Intersections of Surfaces with lSimplexes | 131 |
Intersections of Surfaces with Skeleta | 141 |
Side Approximation Theorem | 151 |
The PL Schoenflies Theorem for | 161 |
Covering Spaces | 175 |
Dehns Lemma | 183 |
Versions of the loop theorem | 203 |
Eliminating branch points | 206 |
Proof of loop theorem | 207 |
History | 210 |
Related Results 1 Approximating 2complexes | 211 |
Approximating homeomorphisms on 3manif0lds | 212 |
Triangulating 3manifolds | 213 |
Locally tame sets are tame | 214 |
Tameness from the side | 215 |
Reembedding crumpled cubes | 217 |
Tame sets in wild surfaces | 218 |
Characterizations | 219 |
Decompositions | 220 |
l0 Other references | 221 |
Appendix Some Standard Results in Topology 1 Metric spaces | 223 |
Planar results | 224 |
Results about 2spheres | 225 |
Cylinders in R3 | 226 |
References 1 | 229 |
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Часто встречающиеся слова и выражения
2-simplex 2-sphere in R3 3-manifold 3-manifold-with-boundary Alexander horned sphere Bd A2 Bd A3 Bd D2 bounded branch point cartesian product cellular Chapter complement component of K2 cone contains covering space crosses crumpled cube defined Dehn disk denote diameter less elements equivalence class extended feelers finite number follows from Theorem fundamental group Hence homeomor homotopy identity Int A2 interior l-ULC lemma lies linear locally connected loop loop theorem map f metric space misses mutually disjoint neighborhood no-triod property odd number open set open subset PL arc PL disk PL homeomorphism PL Schoenflies theorem plane Poincare conjecture point in R3 polygon polyhedral proof of Theorem push S2 F Schoenflies Schoenflies theorem separates shelled shown in Figure shrunk simple closed curve simplex simply-connected singular small disk spanning arc straight arc subdivision Suppose topological triangular disk triangulation union vertex vertices wild sphere