Introduction to 3-manifolds / by Jennifer Schultens.
Material type:
TextSeries: Graduate studies in mathematics ; v. 151Publisher: Providence, Rhode Island : American Mathematical Society, 2014Content type: - text
- computer
- online resource
- 978-1-4704-5471-5 (pbk.)
- Introduction to three-manifolds
- Three-manifolds (Topology)
- Topological manifolds
- Manifolds (Mathematics)
- Manifolds and cell complexes -- Topological manifolds -- Geometric structures on manifolds
- Manifolds and cell complexes -- Topological manifolds -- Neighborhoods of submanifolds
- Manifolds and cell complexes -- Topological manifolds -- General position and transversality
- Manifolds and cell complexes -- PL-topology -- Triangulating manifolds
- Manifolds and cell complexes -- PL-topology -- Comparison of PL-structures: classification, Hauptvermutung
- Manifolds and cell complexes -- PL-topology -- Regular neighborhoods
- Manifolds and cell complexes -- PL-topology -- Knots and links (in high dimensions)
- 514/.34 23
- QA613.2 .S35 2014
- 57N05 | 57N10 | 57N16 | 57N40 | 57N50 | 57N75 | 57Q15 | 57Q25 | 57Q40 | 57Q45
| Item type | Current library | Home library | Collection | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
Book
|
MATH-LiB General Stack | MATH-LiB | NFIC | 514.34 P14 (Browse shelf(Opens below)) | Available | G00022 |
Includes bibliographical references (pages 275-282) and index.
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.
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