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Introduction to 3-manifolds

Author: Jennifer Schultens
Publisher: Providence, Rhode Island : American Mathematical Society, 2014.
Series: Graduate studies in mathematics, v. 151.
Edition/Format:   Print book : EnglishView all editions and formats
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Document Type: Book
All Authors / Contributors: Jennifer Schultens
ISBN: 9781470410209 1470410206
OCLC Number: 863801604
Description: x, 286 pages : illustrations ; 27 cm.
Contents: 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.
Series Title: Graduate studies in mathematics, v. 151.
Other Titles: Introduction to three-manifolds
Responsibility: Jennifer Schultens.

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oaSchultens has written an excellent book that richly illustrates the scope of her chosen subject. It is very well written, clear and explicit in its presentation. There are plenty of exercises, and Read more...

 
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