Representing 3-Manifolds by Filling Dehn Surfaces

Publisher:

World Scientific

Publication Date:

2016

Number of Pages:

300

Format:

Hardcover

Series:

Series on Knots and Everything 58

Price:

132.00

ISBN:

9789814725484

Category:

Monograph

We do not plan to review this book.

Preliminaries:
- Sets
- Manifolds
- Curves
- Transversality
- Regular deformations
- Complexes
Filling Dehn Surfaces:
- Dehn Surfaces in 3-manifolds
- Filling Dehn Surfaces
- Notation
- Surgery on Dehn Surfaces. Montesinos Theorem
Johansson Diagrams:
- Diagrams Associated to Dehn Surfaces
- Abstract Diagrams on Surfaces
- The Johansson Theorem
- Filling Diagrams
Fundamental Group of a Dehn Sphere:
- Coverings of Dehn Spheres
- The Diagram Group
- Coverings and Representations
- Applications
- The Fundamental Group of a Dehn g-torus
Filling Homotopies:
- Filling Homotopies
- Bad Haken Moves
- "Not so Bad" Haken Moves
- Diagram Moves
- Duplication
- Amendola's Moves
Proof of Theorem 5.8:
- Pushing Disks
- Shellings. Smooth Triangulations
- Complex f-moves
- Inflating Triangulations
- Filling Pairs
- Simultaneous Growings
- Proof of Theorem 5.8
The Triple Point Spectrum:
- The Shima's Spheres
- Some Examples of Filling Dehn Surfaces
- The Number of Triple Points as a Measure of Complexity: Montestinos Complexity
- The Triple Point Spectrum
- Surface-complexity
Knots, Knots and Some Open Questions:
- 2-Knots: Lifting Filling Dehn Surfaces
- 1-Knots
- Open Problems