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Representing 3-Manifolds by Filling Dehn Surfaces

Rubén Vigara and Álvaro Lozano-Rojo
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