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• catalog abstract "This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds".
• catalog alternative "Topology and combinatorics of three-manifolds.".
• catalog contributor b8063119.
• catalog created "c1995.".
• catalog date "1995".
• catalog date "c1995.".
• catalog dateCopyrighted "c1995.".
• catalog description "1. Standard Graphs and Meridian-Systems -- 2. The Disc-Complex -- 3. Homeomorphisms -- 4. Pseudo-Anosov Homeomorphisms -- 5. Branching Complexes -- 6. Heegaard-Diagrams -- 7. Surfaces -- 8. Homeomorphisms -- 9. Duality -- 10. Presentations for Surfaces -- 11. The Seifert Characteristic -- 12. Algorithms for Surfaces -- 13. The Haken Spectrum -- 14. Good Pencils -- 15. The Handle-Addition Lemma (Absolute Form) -- 16. The Handle-Addition Lemma (Relative Form) -- 17. Homotopy and Isotopy -- 18. The Mapping Class Group -- 19. Incompressibility -- 20. The Compression-Algorithm -- 21. The Haken Spectrum -- 22. An Example -- 23. The Handle-Addition Lemma (General Case) -- 24. The Unknotting Theorem -- 25. Distances for Heegaard Graphs -- 26. Constructing Heegaard Graphs -- 27. Haken Complexes and Heegaard Complexes -- 28. Short Companions for Haken Graphs -- 29. Invariant Regions for Long Arc-Sequences -- 30. The Universal Limit for Induced Haken Graphs.".
• catalog description "Includes bibliographical references (p.[436]-441) and index.".
• catalog description "This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds".
• catalog extent "xviii, 446 p.".
• catalog hasFormat "Topology and combinatorics of 3-manifolds.".
• catalog identifier "0387590633 (New York : acid-free)".
• catalog identifier "3540590633 (Berlin : acid-free) :".
• catalog isFormatOf "Topology and combinatorics of 3-manifolds.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1599.".
• catalog isPartOf "Lecture notes in mathematics ; 1599".
• catalog issued "1995".
• catalog issued "c1995.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer-Verlag,".
• catalog relation "Topology and combinatorics of 3-manifolds.".
• catalog subject "510 s 514/.223 20".
• catalog subject "Algebraic topology.".
• catalog subject "Cell aggregation Mathematics.".
• catalog subject "Group theory.".
• catalog subject "Mathematics.".
• catalog subject "QA3 .L28 no. 1599 QA613.2".
• catalog subject "Three-manifolds (Topology)".
• catalog tableOfContents "1. Standard Graphs and Meridian-Systems -- 2. The Disc-Complex -- 3. Homeomorphisms -- 4. Pseudo-Anosov Homeomorphisms -- 5. Branching Complexes -- 6. Heegaard-Diagrams -- 7. Surfaces -- 8. Homeomorphisms -- 9. Duality -- 10. Presentations for Surfaces -- 11. The Seifert Characteristic -- 12. Algorithms for Surfaces -- 13. The Haken Spectrum -- 14. Good Pencils -- 15. The Handle-Addition Lemma (Absolute Form) -- 16. The Handle-Addition Lemma (Relative Form) -- 17. Homotopy and Isotopy -- 18. The Mapping Class Group -- 19. Incompressibility -- 20. The Compression-Algorithm -- 21. The Haken Spectrum -- 22. An Example -- 23. The Handle-Addition Lemma (General Case) -- 24. The Unknotting Theorem -- 25. Distances for Heegaard Graphs -- 26. Constructing Heegaard Graphs -- 27. Haken Complexes and Heegaard Complexes -- 28. Short Companions for Haken Graphs -- 29. Invariant Regions for Long Arc-Sequences -- 30. The Universal Limit for Induced Haken Graphs.".
• catalog title "Topology and combinatorics of 3-manifolds / Klaus Johannson.".
• catalog title "Topology and combinatorics of three-manifolds.".
• catalog type "text".