Umfang:
x, 286 Seiten
,
Diagramme
ISBN:
9781470410209
Serie:
Graduate studies in mathematics 151
Inhalt:
1. Perspectives on Manifolds. 1.1. Topological Manifolds -- 1.2. Differentiable Manifolds -- 1.3. Oriented Manifolds -- 1.4. Triangulated Manifolds -- 1.5. Geometric Manifolds -- 1.6. Connected Sums -- 1.7. Equivalence of Categories -- 2. Surfaces. 2.1. A Few Facts about 1-Manifolds -- 2.2. Classification of Surfaces -- 2.3. Decompositions of Surfaces -- 2.4. Covering Spaces and Branched Covering Spaces -- 2.5. Homotopy and Isotopy on Surfaces -- 2.6. The Mapping Class Group -- 3. 3-Manifolds. 3.1. Bundles -- 3.2. The Schonflies Theorem -- 3.3. 3-Manifolds that are Prime but Reducible -- 3.4. Incompressible Surfaces -- 3.5. Dehn's Lemma* -- 3.6. Hierarchies* -- 3.7. Seifert Fibered Spaces -- 3.8. JSJ Decompositions -- 3.9. Compendium of Standard Arguments -- 4. Knots and Links in 3-Manifolds. 4.1. Knots and Links -- 4.2. Reidemeister Moves -- 4.3. Basic Constructions -- 4.4. Knot Invariants -- 4.5. Zoology -- 4.6. Braids -- 4.7. The Alexander Polynomial -- 4.8. Knots and Height Functions -- 4.9. The Knot Group* -- 4.10. Covering Spaces* -- 5. Triangulated 3-Manifolds. 5.1. Simplicial Complexes -- 5.2. Normal Surfaces -- 5.3. Diophantine Systems -- 5.4. 2-Spheres* -- 5.5. Prime Decompositions -- 5.6. Recognition Algorithms -- 5.7. PL Minimal Surfaces** -- 6. Heegaard Splittings. 6.1. Handle Decompositions -- 6.2. Heegaard Diagrams -- 6.3. Reducibility and Stabilization -- 6.4. Waldhausen's Theorem -- 6.5. Structural Theorems -- 6.6. The Rubinstein-Scharlemann Graphic -- 6.7. Weak Reducibility and Incompressible Surfaces -- 6.8. Generalized Heegaard Splittings -- 6.9. An Application -- 6.10. Heegaard Genus and Rank of Fundamental Group* -- 7. Further Topics. 7.1. Basic Hyperbolic Geometry -- 7.2. Hyperbolic n-Manifolds** -- 7.3. Dehn Surgery I -- 7.4. Dehn Surgery II -- 7.5. Foliations -- 7.6. Laminations -- 7.7. The Curve Complex -- 7.8. Through the Looking Glass
Anmerkung:
Literaturverzeichnis: Seiten 275-282
,
1. Perspectives on Manifolds. 1.1. Topological Manifolds1.2. Differentiable Manifolds -- 1.3. Oriented Manifolds -- 1.4. Triangulated Manifolds -- 1.5. Geometric Manifolds -- 1.6. Connected Sums -- 1.7. Equivalence of Categories -- 2. Surfaces. 2.1. A Few Facts about 1-Manifolds -- 2.2. Classification of Surfaces -- 2.3. Decompositions of Surfaces -- 2.4. Covering Spaces and Branched Covering Spaces -- 2.5. Homotopy and Isotopy on Surfaces -- 2.6. The Mapping Class Group -- 3. 3-Manifolds. 3.1. Bundles -- 3.2. The Schonflies Theorem -- 3.3. 3-Manifolds that are Prime but Reducible -- 3.4. Incompressible Surfaces -- 3.5. Dehn's Lemma* -- 3.6. Hierarchies* -- 3.7. Seifert Fibered Spaces -- 3.8. JSJ Decompositions -- 3.9. Compendium of Standard Arguments -- 4. Knots and Links in 3-Manifolds. 4.1. Knots and Links -- 4.2. Reidemeister Moves -- 4.3. Basic Constructions -- 4.4. Knot Invariants -- 4.5. Zoology -- 4.6. Braids -- 4.7. The Alexander Polynomial -- 4.8. Knots and Height Functions -- 4.9. The Knot Group* -- 4.10. Covering Spaces* -- 5. Triangulated 3-Manifolds. 5.1. Simplicial Complexes -- 5.2. Normal Surfaces -- 5.3. Diophantine Systems -- 5.4. 2-Spheres* -- 5.5. Prime Decompositions -- 5.6. Recognition Algorithms -- 5.7. PL Minimal Surfaces** -- 6. Heegaard Splittings. 6.1. Handle Decompositions -- 6.2. Heegaard Diagrams -- 6.3. Reducibility and Stabilization -- 6.4. Waldhausen's Theorem -- 6.5. Structural Theorems -- 6.6. The Rubinstein-Scharlemann Graphic -- 6.7. Weak Reducibility and Incompressible Surfaces -- 6.8. Generalized Heegaard Splittings -- 6.9. An Application -- 6.10. Heegaard Genus and Rank of Fundamental Group* -- 7. Further Topics. 7.1. Basic Hyperbolic Geometry -- 7.2. Hyperbolic n-Manifolds** -- 7.3. Dehn Surgery I -- 7.4. Dehn Surgery II -- 7.5. Foliations -- 7.6. Laminations -- 7.7. The Curve Complex -- 7.8. Through the Looking Glass.
Weitere Ausg.:
Erscheint auch als Online-Ausgabe Schultens, Jennifer, 1965 - Introduction to 3-manifolds Providence, Rhode Island : American Mathematical Society, 2014 ISBN 9781470415587
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Topologische Mannigfaltigkeit
;
Topologische Mannigfaltigkeit
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