Topology and combinatorics of 3-manifolds /

Topology and combinatorics of 3-manifolds /

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Bibliographic Details
Author / Creator:Johannson, Klaus, 1948-
Imprint:Berlin ; New York : Springer-Verlag, ©1995.
Description:1 online resource (xviii, 446 pages) : illustrations.
Language:English
Series:Lecture notes in mathematics, 0075-8434 ; 1599
Lecture notes in mathematics (Springer-Verlag) ; 1599.
Subject:
Three-manifolds (Topology)
Three-manifolds (Topology)
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11071439
Hidden Bibliographic Details
ISBN:9783540491811
3540491813
9780387590639
0387590633
9783540590637
3540590633
Notes:Includes bibliographical references (pages 436-441) and index.
Restrictions unspecified
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212
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Print version record.
Summary: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.
Other form:Print version: Johannson, Klaus, 1948- Topology and combinatorics of 3-manifolds. Berlin ; New York : Springer-Verlag, ©1995 3540590633
Table of Contents:
  • 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.

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