Introduction to 3-manifolds / Jennifer Schultens

By:

Schultens, Jennifer, 1965 [author]

Material type: Text

TextSeries: Graduate studies in mathematics ; 161Publication details: Providence, Rhode Island : New Delhi ; American Mathematical Society, 2019.Description: x, 286 pages : illusstration ; 24 cmISBN:

9781470454715

Subject(s):

DDC classification:

23 514.34 Sch81I

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.

Tags from this library: No tags from this library for this title. Log in to add tags.

Average rating: 0.0 (0 votes)

Holdings
Item type	Current library	Call number	Vol info	Status	Date due	Barcode
Gift Books	Library and Documentation Division PGRRL	514.34 Sch81I (Browse shelf(Opens below))	V. 151	Available		G016878

Gifted by NBHM

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.

There are no comments on this title.

to post a comment.