Algorithmic Topology and Classification of 3-Manifolds

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1 Algorithmic Topology and Classification of 3-Manifolds Bearbeitet von Sergei Matveev Neuausgabe Buch. xiv, 492 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 918 g Weitere Fachgebiete > Mathematik > Numerik und Wissenschaftliches Rechnen Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 1 Simple and Special Polyhedra Spinesof3-Manifolds Collapsing Spines Simple and Special Polyhedra Special Spines Special Polyhedra and Singular Triangulations ElementaryMovesonSpecialSpines Moves on Simple Polyhedra Cell Replacement Lemma Bubble Move Marked Polyhedra Special Polyhedra Which are not Spines Various Notions of Equivalence for Polyhedra Moves on Abstract Simple Polyhedra How to Hit the Target Without Inverse U-Turns Zeeman s Collapsing Conjecture Complexity Theory of 3-Manifolds What is the Complexity of a 3-Manifold? Almost Simple Polyhedra Definition and Estimation of the Complexity Properties of Complexity Converting Almost Simple Spines into Special Ones The Finiteness Property The Additivity Property Closed Manifolds of Small Complexity Enumeration Procedure Simplification Moves Manifolds of Complexity

3 XII 2.4 GraphManifoldsofWaldhausen Properties of Graph Manifolds Manifolds of Complexity Hyperbolic Manifolds Hyperbolic Manifolds of Complexity Lower Bounds of the Complexity Logarithmic Estimates Complexity of Hyperbolic 3-Manifolds Manifolds Having Special Spines with One 2-Cell Haken Theory of Normal Surfaces Basic Notions and Haken s Scheme TheoryofNormalCurves Normal Curves and Normal Equations Fundamental Solutions and Fundamental Curves Geometric Summation An Alternative Approach to the Theory of Normal Curves NormalSurfacesin3-Manifolds Incompressible Surfaces Normal Surfaces in 3-Manifolds with Boundary Pattern Normalization Procedure Fundamental Surfaces Geometric Summation Normal Surfaces in Handle Decompositions Applications of the Theory of Normal Surfaces Examples of Algorithms Based on Haken s Theory Recognition of Splittable Links Getting Rid of Clean Disc Patches Recognizing the Unknot and Calculating the Genus of a Circle in the Boundary of a 3-Manifold Is M 3 Irreducible and Boundary Irreducible? Is a Proper Surface Incompressible and Boundary Incompressible? Is M 3 SufficientlyLarge? Cutting 3-Manifolds along Surfaces Normal Surfaces and Spines Triangulations vs. Handle Decompositions Algorithmic Recognition of S Linksina3-Ball Compressing Discs and One-legged Crowns Thin Position of Links

4 XIII 5.2 TheRubinsteinTheorem Normal Surfaces Proof of the Rubinstein Theorem The Algorithm Classification of Haken 3-Manifolds MainTheorem TheWaldhausenTheorem Deforming Homotopy Equivalences of Surfaces Deforming Homotopy Equivalences of 3-Manifolds to Homeomorphisms Finiteness Properties for Surfaces Two Reformulations of the Recognition Theorem Abstract Extension Moves First Finiteness Property and a Toy Form of the Second Second Finiteness Property for Simple 3-Manifolds Jaco Shalen Johannson Decomposition Improving Isotopy that Separates Surfaces Does M 3 Contain Essential Tori and Annuli? Different Types of Essential Tori and Annuli JSJ-Decomposition Exists and is Unique Seifert and I-Bundle Chambers Third Finiteness Property ExtensionMoves Description of General Extension Moves Structure of Chambers Special Extension Moves: Easy Case Difficult Case Recognition of Simple Stallings Manifolds with Periodic Monodromy Recognition of Simple Stallings Manifolds with Nonperiodic Monodromy Recognition of Quasi-Stallings Manifolds Subdivision of Solid Tori Proof of the Recognition Theorem Manifold Recognizer Computer Presentation of 3-Manifolds Cell Complexes Manifolds as Thickened Spines SimplifyingManifoldsandSpines Coordinate Systems on Tori Reduction of Cell Structures Collapses

5 XIV Surgeries Disc Replacement Moves Labeled Molecules What is a Labeled Molecule? Creating a Labeled Molecule Assembling Seifert Atoms The Algorithm Tabulation Comments on the Table Hyperbolic Manifolds up to Complexity Why the Table Contains no Duplicates? Other Applications of the 3-Manifold Recognizer Enumeration of Heegaard Diagrams of Genus Manifolds Represented by Crystallizations with 32Vertices Classification of Crystallizations of Genus Recognition of Knots and Unknots Two-Step Enumeration of 3-Manifolds Relative Spines and Relative Complexity Assembling Modified Enumeration of Manifolds and Spines The Turaev Viro Invariants TheTuraev ViroInvariants The Construction Turaev Viro Type Invariants of Order r Construction and Properties of the ε-invariant Turaev Viro Invariants of Order r Computing Turaev Viro Invariants More on ε-invariant Manifolds Having the Same Invariants ofturaev ViroType A Appendix A.1 Manifolds of Complexity A.2 Minimal Spines of Manifolds up to Complexity A.3 Minimal Spines of Some Manifolds of Complexity A.4 TablesofTuraev ViroInvariants References Index...489